[{"data":1,"prerenderedAt":26},["ShallowReactive",2],{"post-matrix-binarion":3},{"_id":4,"_path":5,"title":6,"description":7,"date":8,"heroImagePath":9,"tagArr":10,"relatedPost":18,"categoryArr":22,"preface":7,"body":23,"htmlContent":24,"excerptHtml":25},"content:post:matrix-binarion.md","/post/matrix-binarion/","複素数を行列で表現する方法（二元数も）","","2025-12-30T22:45:00+09:00","/img/post/matrix-binarion/hero.png",[11,12,13,14,15,16,17],"research","math","matrix","complex-number","binarion","dual-number","split-complex-number",[19,20,21],"matrix-square-root","collatz-peak-first","fibonacci-word-sequence",[],"\n# 複素数を行列で表現する方法（二元数も）\n\n\n行列で数システムを扱うととても便利なので、備忘録程度に。\n\n結論から言うと、「複素数」をはじめ、「分解型複素数」「二重数」（それらを総称する「二元数」）はすべて行列で表現できます。\n\n\u003C!--more-->\n\n$$\ni = \\left(\n\\begin{array}{cc}\n    0 & -1 \\\\\n    1 &  0 \\\\\n\\end{array}\n\\right), \\\nj = \\left(\n\\begin{array}{cc}\n    0 & 1 \\\\\n    1 & 0 \\\\\n\\end{array}\n\\right) , \\\n\\epsilon = \\left(\n\\begin{array}{cc}\n    0 & 0 \\\\\n    1 & 0 \\\\\n\\end{array}\n\\right)\n$$\n\n## 1とマイナス1\n\nこれが $1$ に相当（単位行列）\n\n$$\n\\left(\n\\begin{array}{cc}\n    1 & 0 \\\\\n    0 & 1 \\\\\n\\end{array}\n\\right)\n$$\n\nこれは $-1$ に相当 ( $-1 \\times -1 = 1$ )\n\n$$\n\\left(\n\\begin{array}{cc}\n    -1 &  0 \\\\\n     0 & -1 \\\\\n\\end{array}\n\\right)\n\\left(\n\\begin{array}{cc}\n    -1 &  0 \\\\\n     0 & -1 \\\\\n\\end{array}\n\\right)\n=\n\\left(\n\\begin{array}{cc}\n    1 & 0 \\\\\n    0 & 1 \\\\\n\\end{array}\n\\right)\n$$\n\n## 虚数単位 i\n\nこれが $i$ に相当 ( $i \\times i = -1$ )\n\n$$\n\\left(\n\\begin{array}{cc}\n    0 & -1 \\\\\n    1 &  0 \\\\\n\\end{array}\n\\right)\n\\left(\n\\begin{array}{cc}\n    0 & -1 \\\\\n    1 &  0 \\\\\n\\end{array}\n\\right)\n=\n\\left(\n\\begin{array}{cc}\n    -1 &  0 \\\\\n     0 & -1 \\\\\n\\end{array}\n\\right)\n$$\n\n対になっているこれが $-i$ に相当 ( $-i \\times -i = -1$ )\n\n$$\n\\left(\n\\begin{array}{cc}\n     0 & 1 \\\\\n    -1 & 0 \\\\\n\\end{array}\n\\right)\n\\left(\n\\begin{array}{cc}\n     0 & 1 \\\\\n    -1 & 0 \\\\\n\\end{array}\n\\right)\n=\n\\left(\n\\begin{array}{cc}\n    -1 &  0 \\\\\n     0 & -1 \\\\\n\\end{array}\n\\right)\n$$\n\n## 分解型複素数の虚数単位 j と二重数の虚数単位 ε\n\nそして、これが分解型複素数の虚数単位 $j$ に相当（2乗したら $1$ になる、 $1$ でも $-1$ でもない数）\n\n$$\n\\left(\n\\begin{array}{cc}\n    0 & 1 \\\\\n    1 & 0 \\\\\n\\end{array}\n\\right)\n\\left(\n\\begin{array}{cc}\n    0 & 1 \\\\\n    1 & 0 \\\\\n\\end{array}\n\\right)\n=\n\\left(\n\\begin{array}{cc}\n    1 & 0 \\\\\n    0 & 1 \\\\\n\\end{array}\n\\right)\n$$\n\nそして、これが二重数の虚数単位 $\\epsilon$ に相当（2乗したら $0$ になる、 $0$ でない数）\n\n$$\n\\left(\n\\begin{array}{cc}\n    0 & 0 \\\\\n    1 & 0 \\\\\n\\end{array}\n\\right)\n\\left(\n\\begin{array}{cc}\n    0 & 0 \\\\\n    1 & 0 \\\\\n\\end{array}\n\\right)\n=\n\\left(\n\\begin{array}{cc}\n    0 & 0 \\\\\n    0 & 0 \\\\\n\\end{array}\n\\right)\n$$\n\n過去の記事では、分解型複素数を指して「2乗すると1になる数」と説明していました。\n\n\u003Carticle-card path=\"/post/matrix-square-root\">\u003C/article-card>","\u003Ch1>複素数を行列で表現する方法（二元数も）\u003C/h1>\n\u003Cp>行列で数システムを扱うととても便利なので、備忘録程度に。\u003C/p>\n\u003Cp>結論から言うと、「複素数」をはじめ、「分解型複素数」「二重数」（それらを総称する「二元数」）はすべて行列で表現できます。\u003C/p>\n\n\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6595em;\">\u003C/span>\u003Cspan class=\"mord mathnormal\">i\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003Cspan class=\"mrel\">=\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003C/span>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:2.4em;vertical-align:-0.95em;\">\u003C/span>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C/span>\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C/span>\u003Cspan class=\"mpunct\">,\u003C/span>\u003Cspan class=\"mspace\"> \u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C/span>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.05724em;\">j\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003Cspan class=\"mrel\">=\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003C/span>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:2.4em;vertical-align:-0.95em;\">\u003C/span>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C/span>\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C/span>\u003Cspan class=\"mpunct\">,\u003C/span>\u003Cspan class=\"mspace\"> \u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C/span>\u003Cspan class=\"mord mathnormal\">ϵ\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003Cspan class=\"mrel\">=\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003C/span>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:2.4em;vertical-align:-0.95em;\">\u003C/span>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C/span>\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\n\u003Ch2>1とマイナス1\u003C/h2>\n\u003Cp>これが \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6444em;\">\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span> に相当（単位行列）\u003C/p>\n\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:2.4em;vertical-align:-0.95em;\">\u003C/span>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C/span>\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\n\u003Cp>これは \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\">\u003C/span>\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span> に相当 ( \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\">\u003C/span>\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C/span>\u003Cspan class=\"mbin\">×\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C/span>\u003C/span>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\">\u003C/span>\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003Cspan class=\"mrel\">=\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003C/span>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6444em;\">\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span> )\u003C/p>\n\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:2.4em;vertical-align:-0.95em;\">\u003C/span>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C/span>\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C/span>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C/span>\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003Cspan class=\"mrel\">=\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003C/span>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:2.4em;vertical-align:-0.95em;\">\u003C/span>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C/span>\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\n\u003Ch2>虚数単位 i\u003C/h2>\n\u003Cp>これが \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6595em;\">\u003C/span>\u003Cspan class=\"mord mathnormal\">i\u003C/span>\u003C/span>\u003C/span>\u003C/span> に相当 ( \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.7429em;vertical-align:-0.0833em;\">\u003C/span>\u003Cspan class=\"mord mathnormal\">i\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C/span>\u003Cspan class=\"mbin\">×\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C/span>\u003C/span>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6595em;\">\u003C/span>\u003Cspan class=\"mord mathnormal\">i\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003Cspan class=\"mrel\">=\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003C/span>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\">\u003C/span>\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span> )\u003C/p>\n\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:2.4em;vertical-align:-0.95em;\">\u003C/span>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C/span>\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C/span>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C/span>\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003Cspan class=\"mrel\">=\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003C/span>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:2.4em;vertical-align:-0.95em;\">\u003C/span>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C/span>\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\n\u003Cp>対になっているこれが \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.7429em;vertical-align:-0.0833em;\">\u003C/span>\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord mathnormal\">i\u003C/span>\u003C/span>\u003C/span>\u003C/span> に相当 ( \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.7429em;vertical-align:-0.0833em;\">\u003C/span>\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord mathnormal\">i\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C/span>\u003Cspan class=\"mbin\">×\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C/span>\u003C/span>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.7429em;vertical-align:-0.0833em;\">\u003C/span>\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord mathnormal\">i\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003Cspan class=\"mrel\">=\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003C/span>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\">\u003C/span>\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span> )\u003C/p>\n\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:2.4em;vertical-align:-0.95em;\">\u003C/span>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C/span>\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C/span>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C/span>\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003Cspan class=\"mrel\">=\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003C/span>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:2.4em;vertical-align:-0.95em;\">\u003C/span>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C/span>\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\n\u003Ch2>分解型複素数の虚数単位 j と二重数の虚数単位 ε\u003C/h2>\n\u003Cp>そして、これが分解型複素数の虚数単位 \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.854em;vertical-align:-0.1944em;\">\u003C/span>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.05724em;\">j\u003C/span>\u003C/span>\u003C/span>\u003C/span> に相当（2乗したら \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6444em;\">\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span> になる、 \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6444em;\">\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span> でも \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\">\u003C/span>\u003Cspan class=\"mord\">−\u003C/span>\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span> でもない数）\u003C/p>\n\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:2.4em;vertical-align:-0.95em;\">\u003C/span>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C/span>\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C/span>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C/span>\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003Cspan class=\"mrel\">=\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003C/span>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:2.4em;vertical-align:-0.95em;\">\u003C/span>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C/span>\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\n\u003Cp>そして、これが二重数の虚数単位 \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.4306em;\">\u003C/span>\u003Cspan class=\"mord mathnormal\">ϵ\u003C/span>\u003C/span>\u003C/span>\u003C/span> に相当（2乗したら \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6444em;\">\u003C/span>\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span> になる、 \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6444em;\">\u003C/span>\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span> でない数）\u003C/p>\n\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:2.4em;vertical-align:-0.95em;\">\u003C/span>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C/span>\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C/span>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C/span>\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003Cspan class=\"mrel\">=\u003C/span>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C/span>\u003C/span>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:2.4em;vertical-align:-0.95em;\">\u003C/span>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C/span>\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C/span>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"vlist-s\">​\u003C/span>\u003C/span>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C/span>\u003C/span>\u003C/span>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\u003C/span>\n\u003Cp>過去の記事では、分解型複素数を指して「2乗すると1になる数」と説明していました。\u003C/p>\n\u003Cdiv class=\"article-card\" style=\"max-width:960px; border:1px solid #e0e0e0; border-radius:8px; padding:12px; margin:16px 0; display:flex; gap:12px; align-items:flex-start;\">\n  \u003Cimg src=\"/img/post/matrix-square-root/hero.png\" alt=\"行列の平方根\" style=\"width:200px; height:125px; object-fit:cover; border-radius:4px; flex-shrink:0;\">\n  \u003Cdiv style=\"flex:1; min-width:0;\">\n    \u003Ca href=\"/post/matrix-square-root\" style=\"text-decoration:none; color:inherit;\">\n      \u003Cdiv style=\"font-size:16px; font-weight:600; line-height:1.2rem; margin-bottom:6px; overflow:hidden; display:-webkit-box; -webkit-line-clamp:2; -webkit-box-orient:vertical;\">行列の平方根\u003C/div>\n      \n      \u003Cdiv style=\"font-size:12px; color:#999; display:flex; align-items:center; gap:8px;\">\u003Cimg src=\"/favicon.ico\" style=\"width:16px;height:16px;\">岩淵夕希物智 公式ブログ\u003C/div>\n    \u003C/a>\n  \u003C/div>\n\u003C/div>","\u003Ch1>複素数を行列で表現する方法（二元数も）\u003C/h1>\n\u003Cp>行列で数システムを扱うととても便利なので、備忘録程度に。\u003C/p>\n\u003Cp>結論から言うと、「複素数」をはじめ、「分解型複素数」「二重数」（それらを総称する「二元数」）はすべて行列で表現できます。\u003C/p>",1768521434101]