{"id":11076,"date":"2022-11-14T15:57:57","date_gmt":"2022-11-14T06:57:57","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=11076"},"modified":"2022-11-17T06:23:11","modified_gmt":"2022-11-16T21:23:11","slug":"imaginary-numbers","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/imaginary-numbers.html","title":{"rendered":"\u865a\u6570\u89e3\u3092\u3082\u3064\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u3068\u5224\u5225\u5f0f"},"content":{"rendered":"\n<p>\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u5834\u5408\u3001\u5fc5\u305a\u3057\u3082\u7b54\u3048\u3092\u5f97\u3089\u308c\u308b\u3068\u306f\u9650\u308a\u307e\u305b\u3093\u3002\u89e3\u306a\u3057\u306e\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u305f\u3060\u865a\u6570\u3092\u5b66\u3093\u3060\u3042\u3068\u3067\u306f\u3001\u89e3\u3092\u5f97\u3089\u308c\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u8a00\u3044\u63db\u3048\u308b\u3068\u3001\u865a\u6570\u3092\u7528\u3044\u3066\u7b54\u3048\u3092\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u8907\u7d20\u6570\u304c\u91cd\u8981\u306a\u306e\u306f\u3001\u305d\u308c\u307e\u3067\u7b54\u3048\u3092\u5f97\u3089\u308c\u306a\u3044\u30b1\u30fc\u30b9\u3067\u3042\u3063\u3066\u3082\u3001\u660e\u78ba\u306a\u7b54\u3048\u3092\u5f97\u3089\u308c\u308b\u304b\u3089\u3067\u3059\u3002<\/p>\n<p>\u7b54\u3048\u304c\u306a\u3044\u5834\u5408\u3001\u660e\u78ba\u306a\u6570\u5b57\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002\u4e00\u65b9\u3067\u8907\u7d20\u6570\u3092\u5229\u7528\u3059\u308c\u3070\u3001\u660e\u78ba\u306a\u6570\u5b57\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u8907\u7d20\u6570\u3092\u5b66\u3076\u5fc5\u8981\u304c\u3042\u308b\u306e\u306f\u3001\u660e\u78ba\u306a\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u3066\u4fbf\u5229\u3060\u304b\u3089\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3067\u865a\u6570\u89e3\u3092\u5f97\u3089\u308c\u308b\u6761\u4ef6\u3084\u5224\u5225\u5f0f\u306e\u6027\u8cea\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306a\u3068\u304d\u306b\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3067\u865a\u6570\u89e3\u3092\u5f97\u3089\u308c\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3067\u306e\u8907\u7d20\u6570\u306e\u95a2\u4fc2\u3084\u8a08\u7b97\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3067\u865a\u6570\u89e3\u3092\u3082\u3064\u30b1\u30fc\u30b9<\/h2>\n<p>\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3067\u865a\u6570\u89e3\u3092\u3082\u3064\u5834\u5408\u3001\u3069\u306e\u3088\u3046\u306a\u7b54\u3048\u306b\u306a\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u5834\u5408\u3001\u56e0\u6570\u5206\u89e3\u3001\u307e\u305f\u306f\u89e3\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u307e\u3059\u3002<\/p>\n<p>\u306a\u304a\u865a\u6570\u89e3\u3092\u3082\u3064\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u89e3\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u307e\u3059\u3002<\/p>\n<p>$$x={-b\\pm\\sqrt{b^2-4ac}\\over2a}$$<\/p>\n<p>\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>\\(x^2+x+1=0\\)<\/li>\n<\/ul>\n<p>\u8907\u7d20\u6570\u3092\u5b66\u3076\u524d\u3067\u3042\u308c\u3070\u3001\u7b54\u3048\u306f\u89e3\u306a\u3057\u3067\u3059\u3002\u4e00\u65b9\u3067\u8907\u7d20\u6570\u3092\u5b66\u3093\u3060\u3042\u3068\u3067\u3042\u308c\u3070\u3001\u660e\u78ba\u306a\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(x=\\displaystyle\\frac{-1\u00b1\\sqrt{1-4}}{2}\\)<\/p>\n<p>\\(x=\\displaystyle\\frac{-1\u00b1\\sqrt{-3}}{2}\\)<\/p>\n<p>\\(x=\\displaystyle\\frac{-1\u00b1\\sqrt{3}i}{2}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7b54\u3048\u306f\\(x=\\displaystyle\\frac{-1\u00b1\\sqrt{3}i}{2}\\)\u3068\u306a\u308a\u307e\u3059\u3002\u7b54\u3048\u306f\u89e3\u306a\u3057\u3067\u306f\u306a\u304f\u3001\u865a\u6570\\(i\\)\u3092\u542b\u3080\u7b54\u3048\u3068\u306a\u308b\u306e\u3067\u3059\u3002<\/p>\n<h3>\u5224\u5225\u5f0f\u3068\u865a\u6570\u89e3\u306e\u5224\u65ad<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306a\u3068\u304d\u306b\u865a\u6570\u89e3\u3092\u5f97\u3089\u308c\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3067\u306f\u5224\u5225\u5f0f\\(D\\)\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u5224\u5225\u5f0f\\(D\\)\u306e\u5024\u304c\u30d7\u30e9\u30b9\u30010\u3001\u30de\u30a4\u30ca\u30b9\u306b\u3088\u3063\u3066\u3001\u89e3\u304c\u5b58\u5728\u3059\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/ydfh2.jpg\" alt=\"\" width=\"463\" height=\"145\" class=\"aligncenter size-full wp-image-4764\" \/><\/p>\n<p>\u305d\u3053\u3067\u8907\u7d20\u6570\u3092\u5b66\u3093\u3060\u3042\u3068\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8003\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\u5224\u5225\u5f0f\\(D\\)\u304c\u6b63\u306e\u5024\uff1a2\u3064\u306e\u5b9f\u6570\u89e3\u3092\u3082\u3064<\/li>\n<li>\u5224\u5225\u5f0f\\(D\\)\u304c0\uff1a1\u3064\u306e\u5b9f\u6570\u89e3\u3092\u3082\u3064\uff08\u91cd\u89e3\uff09<\/li>\n<li><span style=\"color: #0000ff;\">\u5224\u5225\u5f0f\\(D\\)\u304c\u8ca0\u306e\u5024\uff1a2\u3064\u306e\u865a\u6570\u89e3\u3092\u3082\u3064<\/span><\/li>\n<\/ul>\n<p>\\(\\sqrt{-1}=i\\)\u3067\u3042\u308b\u305f\u3081\u3001\u5224\u5225\u5f0f\\(D\\)\u304c\u30de\u30a4\u30ca\u30b9\u306b\u306a\u308b\u5834\u5408\u3001\u865a\u6570\u3092\u5229\u7528\u3057\u3066\u89e3\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<h3>\u5224\u5225\u5f0f\u3092\u7528\u3044\u308b\u865a\u6570\u89e3\u306e\u6761\u4ef6<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u865a\u6570\u89e3\u3092\u3082\u3064\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u306b\u95a2\u3059\u308b\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(x^2+kx+k=0\\)\u3068\\(x^2+(k+1)x+4\\)\u306e\u4e21\u65b9\u3068\u3082\u865a\u6570\u89e3\u3068\u306a\u308b\u5b9a\u6570\\(k\\)\u306e\u7bc4\u56f2\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u4e21\u65b9\u3068\u3082\u865a\u6570\u89e3\u3068\u306a\u308c\u3070\u3044\u3044\u305f\u3081\u3001\u5224\u5225\u5f0f\u304c\u4e21\u65b9\u3068\u3082\\(D&lt;0\\)\u3068\u306a\u308b\u5b9a\u6570\\(k\\)\u306e\u7bc4\u56f2\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><strong>\u30fb\\(x^2+kx+k=0\\)\u306e\u5224\u5225\u5f0f<\/strong><\/p>\n<p>\\(k^2-4k&lt;0\\)<\/p>\n<p>\\(k(k-4)&lt;0\\)<\/p>\n<p>\\(0&lt;k&lt;4\\)<\/p>\n<p><strong>\u30fb\\(x^2+(k+1)x+4\\)\u306e\u5224\u5225\u5f0f<\/strong><\/p>\n<p>\\((k+1)^2-16&lt;0\\)<\/p>\n<p>\\(k^2+2k-15&lt;0\\)<\/p>\n<p>\\((k-3)(k+5)&lt;0\\)<\/p>\n<p>\\(-5&lt;k&lt;3\\)<\/p>\n<p>\\(0&lt;k&lt;4\\)\u3068\\(-5&lt;k&lt;3\\)\u306e\u4e21\u65b9\u3092\u6e80\u305f\u3059\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u7b54\u3048\u306f\\(0&lt;k&lt;3\\)\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<h2>\u4fc2\u6570\u306b\u865a\u6570\u3092\u542b\u3080\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u306e\u51fa\u3057\u65b9<\/h2>\n<p>\u6b21\u306b\u3001\u4fc2\u6570\u306b\u865a\u6570\u3092\u542b\u3080\u5834\u5408\u306e\u89e3\u306e\u51fa\u3057\u65b9\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002\u5224\u5225\u5f0f\\(D\\)\u3092\u5229\u7528\u3059\u308b\u3068\u304d\u3001\u4fc2\u6570\u306f\u5fc5\u305a\u5b9f\u6570\u3067\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002\u4fc2\u6570\u306b\u865a\u6570\u3092\u542b\u3080\u5834\u5408\u3001\u5224\u5225\u5f0f\u3092\u4f7f\u7528\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n<p>\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u5f0f\u306f\u5224\u5225\u5f0f\u3092\u5229\u7528\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n<ul>\n<li>\\((1-i)x^2-(k-i)x+1+ki=0\\)<\/li>\n<\/ul>\n<p>\u305d\u308c\u3067\u306f\u3001\u3053\u306e\u5f0f\u304c\u5b9f\u6570\u89e3\u3092\u3082\u3064\u5834\u5408\u3001\u5b9a\u6570\\(k\\)\u306e\u5024\u3092\u5f97\u308b\u306b\u306f\u3069\u3046\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u4fc2\u6570\u306b\u865a\u6570\u3092\u542b\u3080\u5834\u5408\u3001\u5224\u5225\u5f0f\u3092\u5229\u7528\u305b\u305a\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u5177\u4f53\u7684\u306b\u306f\u3001<span style=\"color: #ff0000;\">\u5b9f\u6570\u89e3\u3092\\(x=\u03b1\\)\u3068\u3057\u307e\u3059\u3002<\/span>\u305d\u306e\u5f8c\u3001\u865a\u6570\\(i\\)\u3092\u57fa\u6e96\u306b\u6574\u7406\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<p>\\((1-i)\u03b1^2-(k+i)\u03b1+1+ki=0\\)<\/p>\n<p>\\((\u03b1^2-k\u03b1+1)-(\u03b1^2+\u03b1-k)i=0\\)<\/p>\n<p>\\(\u03b1\\)\u3068\\(k\\)\u306f\u5b9f\u6570\u3067\u3042\u308b\u305f\u3081\u3001\\(\u03b1^2-k\u03b1+1\\)\u3068\\(\u03b1^2+\u03b1-k\\)\u3082\u5b9f\u6570\u3067\u3059\u3002\u305d\u306e\u305f\u3081\\((\u03b1^2-k\u03b1+1)-(\u03b1^2+\u03b1-k)i=0\\)\u3092\u6e80\u305f\u3059\u305f\u3081\u306b\u306f\u3001\u4ee5\u4e0b\u306e2\u3064\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\u03b1^2-k\u03b1+1=0\\) &#8211; \u2460<\/li>\n<li>\\(\u03b1^2+\u03b1-k=0\\) &#8211; 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