{"id":1302,"date":"2015-10-11T21:53:37","date_gmt":"2015-10-11T12:53:37","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1302"},"modified":"2021-09-29T22:46:10","modified_gmt":"2021-09-29T13:46:10","slug":"tbr201506","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tbr201506\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2015\uff1a\u7b2c6\u554f"},"content":{"rendered":"
\n

\\(\\alpha\\) \u3092\u5b9f\u6570\u3067\u306a\u3044\u8907\u7d20\u6570\u3068\u3057, \\(\\beta\\) \u3092\u6b63\u306e\u5b9f\u6570\u3068\u3059\u308b.\r\n\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. \u305f\u3060\u3057, \u8907\u7d20\u6570 \\(w\\) \u306b\u5bfe\u3057\u3066\u305d\u306e\u5171\u5f79\u8907\u7d20\u6570\u3092 \\(\\overline{w}\\) \u3067\u8868\u3059.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u8907\u7d20\u6570\u5e73\u9762\u4e0a\u3067, \u95a2\u4fc2\u5f0f \\(\\alpha \\overline{z} +\\overline{\\alpha} z = |z|^2\\) \u3092\u6e80\u305f\u3059\u8907\u7d20\u6570 \\(z\\) \u306e\u63cf\u304f\u56f3\u5f62\u3092 \\(C\\) \u3068\u3059\u308b. \u3053\u306e\u3068\u304d, \\(C\\) \u306f\u539f\u70b9\u3092\u901a\u308b\u5186\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u8907\u7d20\u6570\u5e73\u9762\u4e0a\u3067, \\(( z -\\alpha ) ( \\beta -\\overline{\\alpha} )\\) \u304c\u7d14\u865a\u6570\u3068\u306a\u308b\u8907\u7d20\u6570 \\(z\\) \u306e\u63cf\u304f\u56f3\u5f62\u3092 \\(L\\) \u3068\u3059\u308b. \\(L\\) \u306f (1)<\/strong> \u3067\u5b9a\u3081\u305f \\(C\\) \u3068 \\(2\\) \u3064\u306e\u5171\u6709\u70b9\u3092\u3082\u3064\u3053\u3068\u3092\u793a\u305b. \u307e\u305f, \u305d\u306e \\(2\\) \u70b9\u3092 P , Q \u3068\u3059\u308b\u3068\u304d, \u7dda\u5206 PQ \u306e\u9577\u3055\u3092 \\(\\alpha\\) \u3068 \\(\\overline{\\alpha}\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(\\beta\\) \u306e\u8868\u3059\u8907\u7d20\u6570\u5e73\u9762\u4e0a\u306e\u70b9\u3092 R \u3068\u3059\u308b. (2)<\/strong> \u3067\u5b9a\u3081\u305f\u70b9 P , Q \u3068\u70b9 R \u3092\u9802\u70b9\u3068\u3059\u308b\u4e09\u89d2\u5f62\u304c\u6b63\u4e09\u89d2\u5f62\u3067\u3042\u308b\u3068\u304d, \\(\\beta\\) \u3092 \\(\\alpha\\) \u3068 \\(\\overline{\\alpha}\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

    (1)<\/strong><\/p>\r\n

    \u95a2\u4fc2\u5f0f\u3092\u5909\u5f62\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n|z|^2 -\\alpha \\overline{z} -\\overline{\\alpha} z +| \\alpha |^2 & = | \\alpha |^2 \\\\\r\n\\text{\u2234} \\quad | z -\\alpha |^2 & = | \\alpha |^2\r\n\\end{align}\\]\r\n\u3088\u3063\u3066 \\(C\\) \u306f, \u4e2d\u5fc3\u304c\u70b9 \\(\\alpha\\) , \u534a\u5f84 \\(| \\alpha |\\) \u306e\u5186\u3067\u3042\u308a, \u539f\u70b9\u3092\u901a\u308b.<\/p>\r\n

    (2)<\/strong><\/p>\r\n

    \u6761\u4ef6\u3088\u308a\r\n\\[\r\n\\left\\{ \\begin{array}{ll} ( z -\\alpha ) ( \\beta -\\overline{\\alpha} ) +\\overline{( z -\\alpha ) ( \\beta -\\overline{\\alpha} )} = 0 & ... [1] \\\\ ( z -\\alpha ) ( \\beta -\\overline{\\alpha} ) \\neq 0 & ... [2] \\end{array} \\right.\r\n\\]\r\n\u6761\u4ef6\u3088\u308a, \\(\\beta \\neq \\overline{\\alpha}\\) \u306a\u306e\u3067, [2] \u3088\u308a\r\n\\[\r\nz \\neq \\alpha \\quad ... [3]\r\n\\]\r\n\\(\\overline{\\beta} = \\beta\\) \u306b\u6ce8\u610f\u3057\u3066, [1] \u3092\u5909\u5f62\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n( z -\\alpha ) ( \\overline{\\beta -\\alpha} ) +( \\overline{z -\\alpha} ) ( \\beta -\\alpha ) & = 0 \\\\\r\n\\text{\u2234} \\quad \\dfrac{z -\\alpha}{\\beta -\\alpha} +\\overline{\\left( \\dfrac{z -\\alpha}{\\beta -\\alpha} \\right)} & = 0\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(\\dfrac{z -\\alpha}{\\beta -\\alpha}\\) \u306f\u7d14\u865a\u6570\u3067\u3042\u308b\u304b\u3089\r\n\\[\r\n\\text{\u76f4\u7dda} \\ \\alpha z \\perp \\text{\u76f4\u7dda} \\alpha \\beta\r\n\\]\r\n\u3064\u307e\u308a, \\(L\\) \u306f, \u70b9 \\(\\alpha\\) \u3092\u901a\u308a, \u76f4\u7dda \\(\\alpha \\beta\\) \u306b\u5782\u76f4\u306a\u76f4\u7dda\u3067\u3042\u308b.
    \r\n\u3088\u3063\u3066, \\(L\\) \u306f \\(C\\) \u306e\u4e2d\u5fc3\u3092\u901a\u308b\u306e\u3060\u304b\u3089, \\(2\\) \u3064\u306e\u5171\u6709\u70b9\u3092\u3082\u3061, PQ \u306f \\(C\\) \u306e\u76f4\u5f84\u306b\u3042\u305f\u308b\u306e\u3067\r\n\\[\r\n\\text{PQ} = \\underline{2 | \\alpha |}\r\n\\]\r\n

    (3)<\/strong><\/p>\r\n

    \u25b3 PQR \u304c\u6b63\u4e09\u89d2\u5f62\u306a\u306e\u3067\r\n\\[\\begin{gather}\r\n| \\beta -\\alpha | = \\dfrac{\\sqrt{3}}{2} \\cdot 2 | \\alpha | = \\sqrt{3} | \\alpha | \\\\\r\n( \\beta -\\alpha ) ( \\beta -\\overline{\\alpha} ) = 3 \\alpha \\overline{\\alpha} \\\\\r\n{\\beta}^2 -( \\alpha +\\overline{\\alpha} ) \\beta -3 \\alpha \\overline{\\alpha} = 0 \\\\\r\n\\text{\u2234} \\quad \\beta = \\underline{\\dfrac{\\alpha +\\overline{\\alpha} \\pm \\sqrt{{\\alpha}^2 +14 \\alpha \\overline{\\alpha} +{\\overline{\\alpha}}^2 }}{2}}\r\n\\end{gather}\\]\r\n","protected":false},"excerpt":{"rendered":"\\(\\alpha\\) \u3092\u5b9f\u6570\u3067\u306a\u3044\u8907\u7d20\u6570\u3068\u3057, \\(\\beta\\) \u3092\u6b63\u306e\u5b9f\u6570\u3068\u3059\u308b. \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. \u305f\u3060\u3057, \u8907\u7d20\u6570 \\(w\\) \u306b\u5bfe\u3057\u3066\u305d\u306e\u5171\u5f79\u8907\u7d20\u6570\u3092 \\(\\overline{w}\\) \u3067\u8868\u3059. (1)\u3000\u8907 … \u7d9a\u304d\u3092\u8aad\u3080 →<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[132],"tags":[144,137],"class_list":["post-1302","post","type-post","status-publish","format-standard","hentry","category-tsukuba_r_2015","tag-tsukuba_r","tag-137"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1302","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=1302"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1302\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1302"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1302"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1302"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}