{"id":1906,"date":"2021-09-22T21:23:43","date_gmt":"2021-09-22T12:23:43","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=1906"},"modified":"2021-09-22T21:23:43","modified_gmt":"2021-09-22T12:23:43","slug":"tbr201606","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tbr201606\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2016\uff1a\u7b2c6\u554f"},"content":{"rendered":"<hr \/>\n<p>\u8907\u7d20\u6570\u5e73\u9762\u4e0a\u3092\u52d5\u304f\u70b9 \\(z\\) \u3092\u8003\u3048\u308b. \u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\u7b49\u5f0f \\(| z-1 | = | z+1 |\\) \u3092\u6e80\u305f\u3059\u70b9 \\(z\\) \u306e\u5168\u4f53\u306f\u865a\u8ef8\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\u70b9 \\(z\\) \u304c\u539f\u70b9\u3092\u9664\u3044\u305f\u865a\u8ef8\u4e0a\u3092\u52d5\u304f\u3068\u304d, \\(w = \\dfrac{z+1}{z}\\) \u304c\u63cf\u304f\u56f3\u5f62\u306f\u76f4\u7dda\u304b\u3089 \\(1\\) \u70b9\u3092\u9664\u3044\u305f\u3082\u306e\u3068\u306a\u308b. \u3053\u306e\u56f3\u5f62\u3092\u63cf\u3051.<\/p><\/li>\r\n<li><p><strong>(3)<\/strong>\u3000\\(a\\) \u3092\u6b63\u306e\u5b9f\u6570\u3068\u3059\u308b. \u70b9 \\(z\\) \u304c\u865a\u8ef8\u4e0a\u3092\u52d5\u304f\u3068\u304d, \\(w = \\dfrac{za+1}{z-a}\\) \u304c\u63cf\u304f\u56f3\u5f62\u306f\u5186\u304b\u3089 \\(1\\) \u70b9\u3092\u9664\u3044\u305f\u3082\u306e\u3068\u306a\u308b. \u3053\u306e\u5186\u306e\u4e2d\u5fc3\u3068\u534a\u5f84\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\\(z\\) \u306f, \u70b9 \\(1\\) \u3068\u70b9 \\(-1\\) \u306e\u5782\u76f4\u4e8c\u7b49\u5206\u7dda\u3092\u8868\u3059\u306e\u3067, \u865a\u8ef8\u3092\u8868\u3059.<\/p>\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\u6761\u4ef6\u3088\u308a\r\n\\[\\begin{align}\r\nzw & = z+1 \\\\\r\nz ( w-1 ) & = 1\r\n\\end{align}\\]\r\n\\(w \\neq 1\\) ... [1] \u3067\u3042\u308a\r\n\\[\r\nz = \\dfrac{1}{w-1} \\quad ... [2] \\ .\r\n\\]\r\n\\(z\\) \u304c\u865a\u8ef8\u4e0a\u306e\u539f\u70b9\u4ee5\u5916\u3092\u52d5\u304f\u306e\u3067\r\n\\[\r\nz = -\\overline{z} \\quad ... [3] \\ , \\quad z \\neq 0 \\quad ... [4] \\ .\r\n\\]\r\n\u305d\u308c\u305e\u308c\u306b, [2] \u3092\u4ee3\u5165\u3059\u308b\u3068<\/p>\r\n<ul>\r\n<li>[3] \u306b\u3064\u3044\u3066\r\n\\[\\begin{align}\r\n\\dfrac{1}{w-1} & = -\\dfrac{1}{\\overline{w} -1} \\\\\r\n\\overline{w} -1 & = -( w-1 ) \\\\\r\nw +\\overline{w} & = 2 \\\\\r\n\\text{\u2234} \\quad \\mathrm{Re} (w) & = 1\r\n\\end{align}\\]<\/li>\r\n<li>[4] \u306b\u3064\u3044\u3066\r\n\\[\r\n\\dfrac{1}{w-1} \\neq 0\r\n\\]\r\n\u3053\u308c\u306f, \u5e38\u306b\u6210\u7acb\u3059\u308b.<\/p><\/li>\r\n<\/ul>\r\n<p>\u3088\u3063\u3066, \\(w\\) \u306e\u63cf\u304f\u56f3\u5f62\u306f, \u4e0b\u56f3\u306e\u901a\u308a\uff08\u3007\u306f\u9664\u304f\uff09.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/tbr20160601.svg\" alt=\"tbr20160601.svg\" class=\"aligncenter size-full\" \/>\r\n<p><strong>(3)<\/strong><\/p>\r\n<p>\u6761\u4ef6\u3088\u308a\r\n\\[\\begin{align}\r\nz ( w-a ) & = z+1 \\\\\r\nz ( w-1 ) = aw +1\r\n\\end{align}\\]\r\n\\(w \\neq 1\\) ... [5] \u3067\u3042\u308a\r\n\\[\r\nz = \\dfrac{aw +1}{w-1} \\quad ... [6] \\ .\r\n\\]\r\n\\(z\\) \u304c\u865a\u8ef8\u4e0a\u3092\u52d5\u304f\u306e\u3067\r\n\\[\r\nz = -\\overline{z}\r\n\\]\r\n\u3053\u308c\u306b, [6] \u3092\u4ee3\u5165\u3059\u308c\u3070\r\n\\[\\begin{align}\r\n\\dfrac{aw +1}{w-1} & = -\\dfrac{a \\overline{w} +1}{\\overline{w} -1} \\\\\r\n( \\overline{w} -1 ) ( wa +1 ) & = -( w-1 ) ( a \\overline{w} +1 ) \\\\\r\na |w|^2 +\\overline{w} -aw -1 & = -a |w|^2 -w +a \\overline{w} +1 \\\\\r\n2a |w|^2 -(a-1)w -(a-1) \\overline{w} & = 2\r\n\\end{align}\\]\r\n\\(a \\neq 0\\) \u306a\u306e\u3067, \u4e21\u8fba\u3092 \\(2a\\) \u3067\u5272\u3063\u3066\r\n\\[\\begin{align}\r\n\\left( w -\\dfrac{a-1}{2a} \\right) \\left( \\overline{w} -\\dfrac{a-1}{2a} \\right) & = \\dfrac{(a-1)^2}{4a^2} +\\dfrac{1}{a} \\\\\r\n\\left| w -\\dfrac{a-1}{2a} \\right|^2 & = \\dfrac{(a+1)^2}{4a^2} \\\\\r\n\\text{\u2234} \\quad \\left| w -\\dfrac{a-1}{2a} \\right| & = \\dfrac{a+1}{4a}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \\(w\\) \u306e\u63cf\u304f\u56f3\u5f62\u306f, \u70b9 \\(1\\) \u3092\u9664\u3044\u305f\u5186\u3067\u3042\u308a,<br \/>\r\n\u4e2d\u5fc3\u306f, \\(\\underline{\\text{\u70b9} \\ \\dfrac{a-1}{2a}}\\) , \u534a\u5f84\u306f \\(\\underline{\\dfrac{a+1}{4a}}\\) \u3067\u3042\u308b.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\u8907\u7d20\u6570\u5e73\u9762\u4e0a\u3092\u52d5\u304f\u70b9 \\(z\\) \u3092\u8003\u3048\u308b. \u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. (1)\u3000\u7b49\u5f0f \\(| z-1 | = | z+1 |\\) \u3092\u6e80\u305f\u3059\u70b9 \\(z\\) \u306e\u5168\u4f53\u306f\u865a\u8ef8\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b. (2)\u3000\u70b9 \\(z\\) \u304c\u539f\u70b9\u3092\u9664\u3044\u305f\u865a &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/tbr201606\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/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":[158],"tags":[144,162],"class_list":["post-1906","post","type-post","status-publish","format-standard","hentry","category-tsukuba_r_2016","tag-tsukuba_r","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1906","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=1906"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1906\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1906"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1906"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1906"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}