{"id":11061,"date":"2022-11-12T00:56:40","date_gmt":"2022-11-11T15:56:40","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=11061"},"modified":"2022-11-16T05:50:37","modified_gmt":"2022-11-15T20:50:37","slug":"complex-numbers","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/complex-numbers.html","title":{"rendered":"\u8907\u7d20\u6570\uff1a\u5b9f\u6570\u3068\u865a\u6570\u3001\u516c\u5f0f\u3001i\u306e\u4e8c\u4e57\u3001\u8a08\u7b97\u306e\u65b9\u6cd5"},"content":{"rendered":"\n<p>\u9ad8\u6821\u6570\u5b66\u3067\u5b66\u3076\u5185\u5bb9\u306e\u4e00\u3064\u304c\u8907\u7d20\u6570\u3067\u3059\u3002\u8907\u7d20\u6570\u3068\u3044\u3046\u306e\u306f\u3001\u865a\u6570\\(i\\)\uff08Imaginary number\uff09\u3092\u542b\u3080\u6570\u3092\u6307\u3057\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u8907\u7d20\u6570\u3082\u865a\u6570\u3082\u540c\u3058\u6982\u5ff5\u3068\u7406\u89e3\u3059\u308c\u3070\u3044\u3044\u3067\u3059\u3002\u5b9f\u6570\u3068\u865a\u6570\u3092\u5408\u308f\u305b\u305f\u6570\u5b57\u304c\u8907\u7d20\u6570\u3067\u3059\u3002<\/p>\n<p>\u865a\u6570\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u865a\u6570\u306e\u6982\u5ff5\u3092\u5b66\u3070\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002\u865a\u6570\u306e\u516c\u5f0f\u3092\u899a\u3048\u3001\u3069\u306e\u3088\u3046\u306b\u8db3\u3057\u7b97\u3001\u5f15\u304d\u7b97\u3001\u304b\u3051\u7b97\u3001\u5272\u308a\u7b97\u3092\u3059\u308c\u3070\u3044\u3044\u306e\u304b\u7406\u89e3\u3059\u308b\u306e\u3067\u3059\u3002<\/p>\n<p>\u306a\u304a\u3001\u591a\u304f\u306e\u4eba\u306f\u300c\u306a\u305c\u865a\u6570\u3092\u5b66\u3076\u5fc5\u8981\u304c\u3042\u308b\u306e\u304b\uff1f\u300d\u3068\u7591\u554f\u306b\u601d\u3044\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u79c1\u305f\u3061\u304c\u6570\u5b66\u3067\u8907\u7d20\u6570\u3092\u5b66\u3070\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u7406\u7531\u3092\u77e5\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306b\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u8907\u7d20\u6570\u306e\u8a08\u7b97\u3092\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u8907\u7d20\u6570\u306e\u516c\u5f0f\u3084\u5b9a\u7fa9\u3001\u8a08\u7b97\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u5b9f\u5728\u3057\u306a\u3044\u6570\u5b57\u304c\u865a\u6570\uff1a\u4e8c\u4e57\u3059\u308b\u3068-1\u306b\u306a\u308b\u6570<\/h2>\n<p>\u79c1\u305f\u3061\u304c\u5e73\u65b9\u6839\u3092\u5b66\u3076\u3068\u304d\u3001\u300c\u5e73\u65b9\u6839\u306e\u4e2d\u306b\u3042\u308b\u6570\u5b57\u306f\u5fc5\u305a0\u4ee5\u4e0a\u306e\u6570\u306b\u306a\u308b\u300d\u3068\u5b66\u3073\u307e\u3057\u305f\u3002\u4e8c\u4e57\u3059\u308b\u3068\u7b54\u3048\u306f\u5fc5\u305a0\u4ee5\u4e0a\u306e\u6570\u306b\u306a\u308b\u304b\u3089\u3067\u3059\u3002<\/p>\n<p>\u305d\u306e\u305f\u3081\\(\\sqrt{-a}\\)\u306e\u3088\u3046\u306b\u3001\u5e73\u65b9\u6839\u306e\u4e2d\u306b\u30de\u30a4\u30ca\u30b9\u304c\u542b\u307e\u308c\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u5e73\u65b9\u6839\u306b\u30de\u30a4\u30ca\u30b9\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u3068\u3001\u4e8c\u4e57\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u7b54\u3048\u304c\u30de\u30a4\u30ca\u30b9\u3068\u306a\u308a\u3001\u660e\u3089\u304b\u306b\u77db\u76fe\u3059\u308b\u304b\u3089\u3067\u3059\u3002<\/p>\n<ul>\n<li>\\(\\sqrt{-a}^2=-a\\)<\/li>\n<\/ul>\n<p>\u305f\u3060<span style=\"color: #0000ff;\">\u865a\u6570\u3092\u5b66\u3076\u3068\u3001\u5e73\u65b9\u6839\u306e\u4e2d\u304c\u30de\u30a4\u30ca\u30b9\u306b\u306a\u308b\u6570\u5b57\u3092\u5229\u7528\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/span>\u5b9f\u969b\u306b\u306f\u3001\u5e73\u65b9\u6839\u306e\u4e2d\u306b\u3042\u308b\u6570\u5b57\u304c\u30de\u30a4\u30ca\u30b9\u306b\u306a\u308b\u3053\u3068\u306f\u3042\u308a\u5f97\u307e\u305b\u3093\u3002\u3057\u304b\u3057\u3001\u305d\u3046\u3057\u305f\u7a7a\u60f3\u4e0a\u306e\u6570\u5b57\u304c\u5b58\u5728\u3059\u308b\u3068\u8003\u3048\u3001\u865a\u6570\u3092\u5229\u7528\u3059\u308b\u306e\u3067\u3059\u3002<\/p>\n<p>\u865a\u6570\\(i\\)\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(i=\\sqrt{-1}\\)<\/li>\n<\/ul>\n<p><span style=\"color: #ff0000;\">\u4e8c\u4e57\u3059\u308b\u3068-1\u306b\u306a\u308b\u6570\u304c\u865a\u6570\u3067\u3059\u3002<\/span>\u3064\u307e\u308a\u3001\\(i^2=-1\\)\u3067\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u865a\u6570\u3092\u5229\u7528\u3059\u308c\u3070\u3001\u4e8c\u4e57\u306b\u3088\u3063\u3066\u30de\u30a4\u30ca\u30b9\u3068\u306a\u308b\u6570\u5b57\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u865a\u6570\u3092\u5229\u7528\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\sqrt{-4}=4i\\)<\/li>\n<li>\\(\\sqrt{-b}=bi\\)<\/li>\n<li>\\(\\sqrt{-\\displaystyle\\frac{5a+b}{2}}=\\sqrt{\\displaystyle\\frac{5a+b}{2}}i\\)<\/li>\n<\/ul>\n<p>\\(i=\\sqrt{-1}\\)\u3067\u3042\u308b\u3053\u3068\u3092\u77e5\u308c\u3070\u3001\u865a\u6570\u304c\u4f55\u3092\u610f\u5473\u3057\u3066\u3044\u308b\u306e\u304b\u7406\u89e3\u3059\u308b\u306e\u306f\u96e3\u3057\u304f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<h3>\u5b9f\u6570\u3068\u865a\u6570\u306e\u9055\u3044\uff1a\u8907\u7d20\u6570\u306e\u5b9a\u7fa9<\/h3>\n<p>\u3053\u308c\u307e\u3067\u3001\u79c1\u305f\u3061\u304c\u5b66\u3093\u3067\u304d\u305f\u6570\u5b57\u306f\u5b9f\u6570\u3067\u3059\u3002\u6574\u6570\u3084\u5e73\u65b9\u6839\u306f\u5b9f\u5728\u3059\u308b\u5024\u3067\u3059\u3002\u4e00\u65b9\u3067\u5b9f\u5728\u3057\u306a\u3044\u6570\u304c\u865a\u6570\u3067\u3059\u3002\u4e8c\u4e57\u3059\u308b\u3068\u30de\u30a4\u30ca\u30b9\u306b\u306a\u308b\u6570\u306f\u5b58\u5728\u3057\u306a\u3044\u306e\u3067\u3059\u3002<\/p>\n<p>\u3053\u306e\u3068\u304d\u3001\u5b9f\u6570\u3068\u865a\u6570\u306e\u4e21\u65b9\u3092\u5229\u7528\u3057\u3066\u5024\u3092\u8868\u3059\u30b1\u30fc\u30b9\u304c\u591a\u3044\u3067\u3059\u3002\u5b9f\u6570\u3068\u865a\u6570\u3092\u7d44\u307f\u5408\u308f\u305b\u305f\u6982\u5ff5\u304c\u8907\u7d20\u6570\u3067\u3042\u308a\u3001\\(a\\)\u3001\\(b\\)\u3092\u5b9f\u6570\u3068\u3059\u308b\u3068\u3001\u8907\u7d20\u6570\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a+bi\\)<\/li>\n<\/ul>\n<p>\u3082\u3057\\(b=0\\)\u306e\u5834\u5408\u3001\u865a\u6570\u90e8\u5206\u304c\u5b58\u5728\u3057\u306a\u3044\u305f\u3081\u3001\u5024\u306f\u5b9f\u6570\u3067\u3059\u3002\u307e\u305f\\(b\u22600\\)\u306e\u5834\u5408\u3001\u6570\u306f\\(a+bi\\)\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u3001\u3053\u306e\u6570\u3092\u865a\u6570\u3068\u3044\u3044\u307e\u3059\u3002\u306a\u304a\\(a=0\\)\u306e\u5834\u5408\u3001\u7d14\u865a\u6570\u3068\u547c\u3070\u308c\u307e\u3059\u3002<\/p>\n<p>\u53c2\u8003\u307e\u3067\u306b\u3001\u865a\u6570\u306b\u5927\u5c0f\u95a2\u4fc2\u306f\u3042\u308a\u307e\u305b\u3093\u3002<span style=\"color: #0000ff;\">\u865a\u6570\u306b\u6b63\u306e\u6570\u3084\u8ca0\u306e\u6570\u306f\u5b58\u5728\u3057\u306a\u3044\u306e\u3067\u3059\u3002<\/span>\u865a\u6570\u3068\u3044\u3046\u306e\u306f\u3001\u3042\u304f\u307e\u3067\u3082\u7a7a\u60f3\u4e0a\u306e\u6570\u306b\u3059\u304e\u307e\u305b\u3093\u3002<\/p>\n<h3>\u306a\u305c\u865a\u6570\u3092\u5b66\u3076\u5fc5\u8981\u304c\u3042\u308b\u306e\u304b<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u306a\u305c\u79c1\u305f\u3061\u306f\u6570\u5b66\u3067\u865a\u6570\u3092\u5b66\u3076\u5fc5\u8981\u304c\u3042\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u5b9f\u5728\u3057\u306a\u3044\u6570\u3092\u5229\u7528\u3059\u308b\u610f\u5473\u306f\u306a\u3044\u3068\u8003\u3048\u308b\u4eba\u306f\u591a\u3044\u3067\u3059\u3002\u865a\u6570\u3092\u5b66\u3076\u7406\u7531\u306f\u7c21\u5358\u3067\u3042\u308a\u3001\u4fbf\u5229\u3060\u304b\u3089\u3067\u3059\u3002\u8981\u306f\u3001\u5e73\u65b9\u6839\u3092\u5b66\u3076\u7406\u7531\u3068\u540c\u3058\u3067\u3059\u3002<\/p>\n<p>\u5e73\u65b9\u6839\u3092\u5b66\u3076\u524d\u3067\u306f\u3001\u591a\u304f\u306e\u4eba\u306f\u7121\u7406\u6570\u306e\u6982\u5ff5\u3092\u7406\u89e3\u3057\u3066\u3044\u307e\u305b\u3093\u3002\u305f\u3060\u5e73\u65b9\u6839\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u89d2\u5ea6\u306e\u8a08\u7b97\u3092\u3057\u305f\u308a\u3001\u4e09\u5e73\u65b9\u306e\u5b9a\u7406\u3092\u5229\u7528\u3057\u305f\u308a\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\u6570\u5b66\u3067\u591a\u304f\u306e\u4eba\u304c\u5f53\u305f\u308a\u524d\u306e\u3088\u3046\u306b\u5e73\u65b9\u6839\u3092\u5229\u7528\u3057\u3066\u3044\u308b\u306e\u306f\u3001\u5e73\u65b9\u6839\u304c\u4fbf\u5229\u3060\u304b\u3089\u3067\u3059\u3002<\/p>\n<p>\u865a\u6570\u3082\u540c\u69d8\u3067\u3042\u308a\u3001\u8a08\u7b97\u3059\u308b\u3068\u304d\u306b\u865a\u6570\u3092\u5229\u7528\u3059\u308b\u3068\u4fbf\u5229\u3067\u3059\u3002\u7279\u306b\u5927\u5b66\u306e\u7269\u7406\u3067\u306f\u3001\u8a08\u7b97\u904e\u7a0b\u3067\u865a\u6570\u304c\u5f53\u7136\u306e\u3088\u3046\u306b\u51fa\u3066\u304d\u307e\u3059\u3002\u865a\u6570\u3092\u5b66\u3093\u3067\u3044\u306a\u3044\u3068\u8a08\u7b97\u3067\u304d\u306a\u3044\u3082\u306e\u306e\u3001\u865a\u6570\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u7b54\u3048\u3092\u5f97\u3089\u308c\u308b\u3088\u3046\u306b\u306a\u308b\u306e\u3067\u3059\u3002<\/p>\n<p>\u7269\u7406\u3068\u3044\u3046\u306e\u306f\u3001\u8907\u7d20\u6570\u3092\u5229\u7528\u3057\u306a\u3044\u3068\u6a5f\u80fd\u3057\u307e\u305b\u3093\u3002\u865a\u6570\u3092\u5229\u7528\u3059\u308b\u304b\u3089\u3053\u305d\u3001\u7269\u7406\u304c\u767a\u5c55\u3057\u3066\u3044\u308b\u306e\u3067\u3059\u3002<\/p>\n<h2>\u8907\u7d20\u6570\u3092\u5229\u7528\u3057\u3066\u8db3\u3057\u7b97\u3001\u5f15\u304d\u7b97\u3092\u8a08\u7b97\u3059\u308b<\/h2>\n<p>\u305d\u308c\u3067\u306f\u3001\u8907\u7d20\u6570\u3092\u5229\u7528\u3057\u3066\u8db3\u3057\u7b97\u3068\u5f15\u304d\u7b97\u3092\u884c\u3048\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u5b9f\u6570\u3068\u865a\u6570\u306f\u307e\u3063\u305f\u304f\u7570\u306a\u308b\u6982\u5ff5\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u5b9f\u6570\u90e8\u5206\u3068\u865a\u6570\u90e8\u5206\u3092\u308f\u3051\u3066\u8db3\u3057\u7b97\u307e\u305f\u306f\u5f15\u304d\u7b97\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u30eb\u30fc\u30c8\u306e\u8db3\u3057\u7b97\u3092\u3059\u308b\u3068\u304d\u3067\u3042\u3063\u3066\u3082\u3001\u6574\u6570\u3068\u30eb\u30fc\u30c8\u3092\u308f\u3051\u3066\u8db3\u3057\u7b97\u3092\u3057\u307e\u3059\u3002\u540c\u3058\u3088\u3046\u306b\u8003\u3048\u3001\u5b9f\u6570\u3068\u865a\u6570\u306f\u7570\u306a\u308b\u90e8\u5206\u3067\u3042\u308b\u3068\u6349\u3048\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n<p>\u305d\u306e\u305f\u3081\u8907\u7d20\u6570\u306e\u8db3\u3057\u7b97\u3068\u5f15\u304d\u7b97\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\((a+bi)+(c+di)=a+c+(b+d)i\\)<\/li>\n<li>\\((a+bi)-(c+di)=a-c+(b-d)i\\)<\/li>\n<\/ul>\n<p>\u4f8b\u3048\u3070\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\((4+2i)+(5+i)=9+3i\\)<\/li>\n<li>\\((4+2i)-(5+i)=-1+i\\)<\/li>\n<\/ul>\n<p>\u5b9f\u6570\u90e8\u5206\u3068\u865a\u6570\u90e8\u5206\u3092\u5206\u3051\u3066\u8db3\u3057\u7b97\u307e\u305f\u306f\u5f15\u304d\u7b97\u3092\u3059\u308c\u3070\u3044\u3044\u305f\u3081\u3001\u554f\u984c\u306a\u304f\u8a08\u7b97\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<h3>\u865a\u6570\u3092\u5229\u7528\u3059\u308b\u304b\u3051\u7b97<\/h3>\n<p>\u6b21\u306b\u8907\u7d20\u6570\u306e\u304b\u3051\u7b97\u3068\u5272\u308a\u7b97\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002\u5e73\u65b9\u6839\u3067\u306f\u3001\u6574\u6570\u3084\u30eb\u30fc\u30c8\u306b\u95a2\u4fc2\u306a\u304f\u304b\u3051\u7b97\u3092\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u540c\u3058\u3088\u3046\u306b\u3001<span style=\"color: #0000ff;\">\u865a\u6570\u306b\u3064\u3044\u3066\u3082\u5206\u914d\u6cd5\u5247\u3092\u5229\u7528\u3057\u3066\u304b\u3051\u7b97\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n<ul>\n<li>\\((a+bi)(c+di)=(ac-bd)\\)\\(+(ad+bc)i\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/idjw2.jpg\" alt=\"\" width=\"380\" height=\"151\" class=\"aligncenter size-full wp-image-11065\" \/><\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u8a08\u7b97\u3092\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\((1+2i)(3-4i)\\)<\/li>\n<\/ul>\n<p>\u5206\u914d\u6cd5\u5247\u3092\u5229\u7528\u3057\u3066\u5c55\u958b\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\((1+2i)(3-4i)\\)<\/p>\n<p>\\(=3-4i+6i-8i^2\\)<\/p>\n<p>\\(=11+2i\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u865a\u6570\u3092\u542b\u3080\u304b\u3051\u7b97\u3067\u306f\u3001\u516c\u5f0f\u3092\u899a\u3048\u3066\u3082\u3044\u3044\u3057\u3001\u5206\u914d\u6cd5\u5247\u3092\u6bce\u56de\u5229\u7528\u3057\u3066\u3082\u3044\u3044\u3067\u3059\u3002<\/p>\n<h3>\u5206\u6bcd\u306e\u5b9f\u6570\u5316\uff1a\u8907\u7d20\u6570\u306e\u5272\u308a\u7b97<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u8907\u7d20\u6570\u306e\u5272\u308a\u7b97\u306f\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u308f\u308a\u7b97\u3068\u3044\u3046\u306e\u306f\u3001\u5206\u6570\u3067\u3082\u3042\u308a\u307e\u3059\u3002<span style=\"color: #0000ff;\">\u865a\u6570\u3092\u542b\u3080\u5206\u6570\uff08\u5272\u308a\u7b97\uff09\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u5206\u6bcd\u3092\u5b9f\u6570\u306b\u5909\u3048\u307e\u3057\u3087\u3046\u3002<\/span>\u5229\u7528\u3059\u308b\u516c\u5f0f\u306f\u4ee5\u4e0b\u3067\u3059\u3002<\/p>\n<ul>\n<li>\\((a+b)(a-b)=a^2-b^2\\)<\/li>\n<\/ul>\n<p>\u3042\u306a\u305f\u304c\u65e2\u306b\u77e5\u3063\u3066\u3044\u308b\u3053\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u5206\u6bcd\u3092\u5b9f\u6570\u306b\u3059\u308b\u306e\u3067\u3059\u3002\u4f8b\u984c\u3068\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u5206\u6570\uff08\u8907\u7d20\u6570\u306e\u5272\u308a\u7b97\uff09\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle\\frac{1+2i}{2+3i}\\)<\/li>\n<\/ul>\n<p>\u5206\u6bcd\u3092\u5b9f\u6570\u5316\u3059\u308b\u305f\u3081\u3001\u5206\u5b50\u3068\u5206\u6bcd\u306b\\((2-3i)\\)\u3092\u304b\u3051\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle\\frac{1+2i}{2+3i}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{(1+2i)(2-3i)}{(2+3i)(2-3i)}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{2-3i+4i-6i^2}{4-9i^2}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{8+i}{13}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5206\u6bcd\u306e\u5b9f\u6570\u5316\u306b\u3088\u3063\u3066\u8907\u7d20\u6570\u306e\u5272\u308a\u7b97\u3092\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h3>\u8907\u7d20\u6570\u306e\u6761\u4ef6\u3068\u8a08\u7b97\u554f\u984c<\/h3>\n<p>\u3053\u3053\u307e\u3067\u3001\u8907\u7d20\u6570\u306e\u8a08\u7b97\u3092\u3059\u308b\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u3066\u304d\u307e\u3057\u305f\u3002\u3053\u308c\u3089\u306e\u6761\u4ef6\u3092\u5229\u7528\u3057\u3066\u3001\u8a08\u7b97\u554f\u984c\u3092\u89e3\u3051\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\u4e8c\u4e57\u3057\u3066\\(6i\\)\u3068\u306a\u308b\u8907\u7d20\u6570\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u8907\u7d20\u6570\u306e\u5b9a\u7fa9\u306f\\(a+bi\\)\u3067\u3042\u308a\u3001\\(a\\)\u3068\\(b\\)\u306f\u5b9f\u6570\u3067\u3059\u3002<span style=\"color: #ff0000;\">\\(a\\)\u3068\\(b\\)\u304c\u5b9f\u6570\u3067\u3042\u308b\u3053\u3068\u306f\u91cd\u8981\u3067\u3042\u308a\u3001\u3053\u306e\u524d\u63d0\u6761\u4ef6\u304c\u306a\u3044\u3068\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002<\/span>\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u4e8c\u4e57\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\((a+bi)^2\\)<\/p>\n<p>\\(=a^2+2abi+b^2i^2\\)<\/p>\n<p>\\(=(a^2-b^2)+2abi\\)<\/p>\n<p>\u4e8c\u4e57\u3057\u3066\\(6i\\)\u3068\u306a\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e2\u3064\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3055\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n<ul>\n<li>\\(a^2-b^2=0\\)<\/li>\n<li>\\(2ab=6\\)<\/li>\n<\/ul>\n<p>\\(a^2=b^2\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(a=\u00b1b\\)\u3067\u3059\u3002\u305d\u3053\u3067\u3001\\(a=b\\)\u3068\\(a=-b\\)\u3067\u5834\u5408\u5206\u3051\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><strong>\u30fb\\(a=b\\)\u306e\u5834\u5408<\/strong><\/p>\n<p>\\(2ab=6\\)\u3001\u3064\u307e\u308a\\(ab=3\\)\u3092\u6e80\u305f\u3059\\(a\\)\u3068\\(b\\)\u306f\u4ee5\u4e0b\u306e2\u901a\u308a\u3067\u3059\u3002<\/p>\n<ul>\n<li>\\(a=\\sqrt{3}\\)\u3001\\(b=\\sqrt{3}\\)<\/li>\n<li>\\(a=-\\sqrt{3}\\)\u3001\\(b=-\\sqrt{3}\\)<\/li>\n<\/ul>\n<p>\u305d\u306e\u305f\u3081\u3001\\(\\sqrt{3}+\\sqrt{3}i\\)\u3068\\(-\\sqrt{3}-\\sqrt{3}i\\)\u304c\u7b54\u3048\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p><strong>\u30fb\\(a=-b\\)\u306e\u5834\u5408<\/strong><\/p>\n<p>\\(ab=3\\)\u3092\u6e80\u305f\u3059\\(a\\)\u3068\\(b\\)\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u7570\u306a\u308b\u7b26\u53f7\u306e\u5b9f\u6570\u3092\u304b\u3051\u3066\u30d7\u30e9\u30b9\u306e\u7b54\u3048\u306b\u306a\u308b\u3053\u3068\u306f\u306a\u3044\u306e\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u89e3\u306a\u3057\u3067\u3059\u3002<\/p>\n<p>\u4ee5\u4e0a\u306e\u8a08\u7b97\u7d50\u679c\u3088\u308a\u3001\u7b54\u3048\u306f\\(\\sqrt{3}+\\sqrt{3}i\\)\u3068\\(-\\sqrt{3}-\\sqrt{3}i\\)\u3067\u3059\u3002<\/p>\n<h2>\u8907\u7d20\u6570\u306e\u6982\u5ff5\u3092\u77e5\u308a\u3001\u865a\u6570\u3092\u5229\u7528\u3067\u304d\u308b\u3088\u3046\u306b\u3059\u308b<\/h2>\n<p>\u591a\u304f\u306e\u4eba\u304c\u6df7\u4e71\u3059\u308b\u5185\u5bb9\u306e\u4e00\u3064\u304c\u865a\u6570\u3067\u3059\u3002\u5b9f\u5728\u3057\u306a\u3044\u6570\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u3001\u865a\u6570\u306b\u5927\u5c0f\u95a2\u4fc2\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u305d\u306e\u305f\u3081\u3001\u306a\u305c\u5b9f\u5728\u3057\u306a\u3044\u6570\u3092\u5b66\u3076\u5fc5\u8981\u304c\u3042\u308b\u306e\u304b\u7406\u89e3\u3067\u304d\u306a\u3044\u306e\u3067\u3059\u3002<\/p>\n<p>\u305f\u3060\u3001\u865a\u6570\u306f\u5927\u5b66\u3067\u5b66\u3076\u79d1\u5b66\u3067\u5fc5\u9808\u3068\u306a\u308b\u6982\u5ff5\u3067\u3059\u3002\u7279\u306b\u7269\u7406\u3067\u306f\u3001\u5fc5\u305a\u865a\u6570\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002\u865a\u6570\u304c\u3042\u308b\u3068\u8a08\u7b97\u3067\u304d\u308b\u7bc4\u56f2\u304c\u5e83\u304f\u306a\u308a\u3001\u975e\u5e38\u306b\u4fbf\u5229\u306a\u306e\u3067\u3059\u3002<\/p>\n<p>\u305d\u3053\u3067\u3001\u865a\u6570\\(i\\)\u304c\u4f55\u3092\u610f\u5473\u3057\u3066\u3044\u308b\u306e\u304b\u5b66\u3073\u307e\u3057\u3087\u3046\u3002\u307e\u305f\u3001\u8907\u7d20\u6570\u306e\u5b9a\u7fa9\u3092\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002\u8907\u7d20\u6570\u306f\u5b9f\u6570\u90e8\u5206\u3068\u865a\u6570\u90e8\u5206\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u307e\u305f\u8907\u7d20\u6570\u306e\u8db3\u3057\u7b97\u3001\u5f15\u304d\u7b97\u3001\u304b\u3051\u7b97\u3001\u308f\u308a\u7b97\u306b\u306f\u8a08\u7b97\u65b9\u6cd5\u304c\u3042\u308a\u3001\u56db\u5247\u6f14\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u65b0\u305f\u306a\u6982\u5ff5\u304c\u865a\u6570\u3067\u3042\u308b\u3082\u306e\u306e\u3001\u8a08\u7b97\u65b9\u6cd5\u306f\u96e3\u3057\u304f\u3042\u308a\u307e\u305b\u3093\u3002\u8a08\u7b97\u306b\u4fbf\u5229\u306a\u30c4\u30fc\u30eb\u3068\u3057\u3066\u3001\u865a\u6570\\(i\\)\u3092\u5229\u7528\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u9ad8\u6821\u6570\u5b66\u3067\u5b66\u3076\u5185\u5bb9\u306e\u4e00\u3064\u304c\u8907\u7d20\u6570\u3067\u3059\u3002\u8907\u7d20\u6570\u3068\u3044\u3046\u306e\u306f\u3001\u865a\u6570\\(i\\)\uff08Imaginary number\uff09\u3092\u542b\u3080\u6570\u3092\u6307\u3057\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u8907\u7d20\u6570\u3082\u865a\u6570\u3082\u540c\u3058\u6982\u5ff5\u3068\u7406\u89e3\u3059\u308c\u3070\u3044\u3044\u3067\u3059\u3002\u5b9f\u6570\u3068\u865a\u6570\u3092\u5408\u308f\u305b\u305f\u6570\u5b57\u304c\u8907\u7d20\u6570\u3067\u3059\u3002  [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":11073,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[],"class_list":{"0":"post-11061","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-h-math"},"_links":{"self":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/11061","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/comments?post=11061"}],"version-history":[{"count":8,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/11061\/revisions"}],"predecessor-version":[{"id":11103,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/11061\/revisions\/11103"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media\/11073"}],"wp:attachment":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media?parent=11061"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/categories?post=11061"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/tags?post=11061"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}