{"id":790,"date":"2023-07-16T12:35:39","date_gmt":"2023-07-16T09:35:39","guid":{"rendered":"https:\/\/bagrut-ru.com\/?p=790"},"modified":"2025-09-04T17:43:41","modified_gmt":"2025-09-04T14:43:41","slug":"%d0%b1%d0%b0%d0%b3%d1%80%d1%83%d1%82-5-%d0%bb%d0%b5%d1%82%d0%be-2023-%d0%b2%d0%b0%d1%80%d0%b8%d0%b0%d0%bd%d1%82-35582-%d0%b7%d0%b0%d0%b4%d0%b0%d0%bd%d0%b8%d0%b5-3","status":"publish","type":"post","link":"https:\/\/bagrut-ru.com\/?p=790","title":{"rendered":"\u0411\u0410\u0413\u0420\u0423\u0422 (5). \u041b\u0415\u0422\u041e 2023, \u0412\u0410\u0420\u0418\u0410\u041d\u0422 35582, \u0417\u0410\u0414\u0410\u041d\u0418\u0415 3"},"content":{"rendered":"\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"553\" data-id=\"791\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/66-1024x553.png\" alt=\"\" class=\"wp-image-791\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/66-1024x553.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/66-300x162.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/66-768x414.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/66.png 1412w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-2 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"653\" data-id=\"792\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/67-1024x653.png\" alt=\"\" class=\"wp-image-792\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/67-1024x653.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/67-300x191.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/67-768x490.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/67.png 1442w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/meyda.education.gov.il\/sheeloney_bagrut\/2023\/6\/RUS\/35582.pdf\" data-type=\"link\" data-id=\"https:\/\/meyda.education.gov.il\/sheeloney_bagrut\/2023\/6\/RUS\/35582.pdf\">\u0438\u0441\u0442\u043e\u0447\u043d\u0438\u043a<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><div class=\"spoiler-wrap\">\n\t\t\t\t<div class=\"spoiler-head folded\">\u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/div>\n\t\t\t\t<div class=\"spoiler-body\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\"><strong>(<\/strong><\/mark><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\u05d0) <\/mark><\/strong>\u041d\u0430\u0439\u0434\u0435\u043c \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043a\u043e\u0440\u043d\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \\(z^3=\\frac{1}{z^3}\\)<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u041a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e  \\(z=a+i\\ b\\) \u043c\u043e\u0436\u043d\u043e \u0438\u0437\u043e\u0431\u0440\u0430\u0437\u0438\u0442\u044c \u043d\u0430 \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0413\u0430\u0443\u0441\u0441\u0430. \\(a,b\\) &#8212; \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0442\u043e\u0447\u043a\u0438. (\u0440\u0438\u0441. 1)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"> <\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-3 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"460\" data-id=\"832\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/74.png\" alt=\"\" class=\"wp-image-832\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/74.png 720w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/74-300x192.png 300w\" sizes=\"auto, (max-width: 720px) 100vw, 720px\" \/><figcaption class=\"wp-element-caption\">\u0440\u0438\u0441. 1<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"wp-block-paragraph\"> \u041a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u0432 <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u043e\u0440\u043c\u0435 <\/mark><\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\\(z=|z|(\\cos \\phi+i\\ \\sin \\phi )\\). <\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0417\u0434\u0435\u0441\u044c \\(|z|=\\sqrt{a^2+b^2}\\) &#8212; \u043c\u043e\u0434\u0443\u043b\u044c \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430, \\(\\phi\\) &#8212;    \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442 \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430. \u0410\u0440\u0433\u0443\u043c\u0435\u043d\u0442 \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430 \u043c\u043e\u0436\u043d\u043e \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0440\u0430\u0437\u0438\u0442\u044c \u0432 \u0433\u0440\u0430\u0434\u0443\u0441\u0430\u0445 \u0438\u043b\u0438 \u0432 \u0440\u0430\u0434\u0438\u0430\u043d\u0430\u0445. \u041d\u0430\u0439\u0442\u0438 \u0435\u0433\u043e \u043c\u043e\u0436\u043d\u043e, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0442\u0430\u043a. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"> \\(\\phi=arctg {\\frac{b}{a}}\\), \u0435\u0441\u043b\u0438 \\(a&gt;0\\), ( 1 \u0438 4 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u043d\u044b\u0435 \u0447\u0435\u0442\u0432\u0435\u0440\u0442\u0438, \u0440\u0438\u0441. 2 \u0438  \u0440\u0438\u0441. 3) <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\\\\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\\\\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\\\\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\\\\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\\\\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\\\\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\\\\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\\\\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\\\\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\\\\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\phi=\\pi +arctg {\\frac{b}{a}}\\), \u0435\u0441\u043b\u0438 \\(a&lt;0, \\ b&gt;0\\), ( 2 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u043d\u0430\u044f \u0447\u0435\u0442\u0432\u0435\u0440\u0442\u044c, \u0440\u0438\u0441. 4) <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\\\\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\\\\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\\\\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\\\\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\phi=-\\pi +arctg {\\frac{b}{a}}\\), \u0435\u0441\u043b\u0438 \\(a&lt;0, \\ b&lt;0\\), ( 3 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u043d\u0430\u044f \u0447\u0435\u0442\u0432\u0435\u0440\u0442\u044c, \u0440\u0438\u0441. 5) <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-4 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"440\" data-id=\"811\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/69-1.png\" alt=\"\" class=\"wp-image-811\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/69-1.png 720w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/69-1-300x183.png 300w\" sizes=\"auto, (max-width: 720px) 100vw, 720px\" \/><figcaption class=\"wp-element-caption\">\u0440\u0438\u0441.2<\/figcaption><\/figure>\n<\/figure>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-5 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"698\" height=\"626\" data-id=\"814\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/73-1.png\" alt=\"\" class=\"wp-image-814\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/73-1.png 698w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/73-1-300x269.png 300w\" sizes=\"auto, (max-width: 698px) 100vw, 698px\" \/><figcaption class=\"wp-element-caption\">\u0440\u0438\u0441. 3<\/figcaption><\/figure>\n<\/figure>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-6 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"718\" height=\"438\" data-id=\"815\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/70-2.png\" alt=\"\" class=\"wp-image-815\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/70-2.png 718w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/70-2-300x183.png 300w\" sizes=\"auto, (max-width: 718px) 100vw, 718px\" \/><figcaption class=\"wp-element-caption\">\u0440\u0438\u0441. 4<\/figcaption><\/figure>\n<\/figure>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-7 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"710\" height=\"608\" data-id=\"842\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/75.png\" alt=\"\" class=\"wp-image-842\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/75.png 710w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/75-300x257.png 300w\" sizes=\"auto, (max-width: 710px) 100vw, 710px\" \/><figcaption class=\"wp-element-caption\">\u0440\u0438\u0441.5<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u0412\u0435\u0440\u043d\u0435\u043c\u0441\u044f \u043a \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e \\(z^3=\\frac{1}{z^3}\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0420\u0435\u0448\u0438\u043c \u0435\u0433\u043e. \u041f\u0435\u0440\u0435\u043d\u0435\u0441\u0435\u043c \u0432\u0441\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435 \u0432\u043b\u0435\u0432\u043e \u0438 \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043c \u043a \u043e\u0431\u0449\u0435\u043c\u0443 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044e. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(z^3-\\frac{1}{z^3}=0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\frac{z^6-1}{z^3}=0\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0414\u0440\u043e\u0431\u044c \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e, \u043a\u043e\u0433\u0434\u0430 \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e, \u0430 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u043d\u0435 \u0440\u0430\u0432\u0435\u043d. \u041f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0441\u0438\u0441\u0442\u0435\u043c\u0443: <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\( \\Bigg \\{ \\begin {matrix} {z^6-1=0}\\\\{z^3\\ne 0}\\end {matrix}\\);  \\( \\Bigg \\{ \\begin {matrix} {z^6=1}\\\\{z^3\\ne 0}\\end {matrix}\\); \\( \\Bigg \\{ \\begin {matrix} {z=\\sqrt[6]{1}}\\\\{z\\ne \\sqrt[3]{0}}\\end {matrix}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"> \u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\\(z=\\sqrt[n]{w}\\)<\/mark> \u0438\u043c\u0435\u0435\u0442 \u0440\u043e\u0432\u043d\u043e \\(n\\) \u043a\u043e\u0440\u043d\u0435\u0439 \\(z_0,\\ z_1,\\ z_2,\\ &#8230;z_{n-1}\\), \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u043e\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\\(z_k=\\sqrt[n]{|w|}(\\cos {\\frac{\\phi +2\\pi k}{n}}+i\\ \\sin {\\frac{\\phi +2\\pi k}{n}})\\), <\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0433\u0434\u0435 \\(|w|\\) &#8212; \u044d\u0442\u043e \u043c\u043e\u0434\u0443\u043b\u044c \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430 \\(w\\), \\(\\phi \\) &#8212; \u0435\u0433\u043e \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442, \u0430 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440 \\(k\\) \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u0435\u0442 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f  \\(\\{0,\\ 1,\\ &#8230;n-1\\}\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u0447\u0438\u0441\u043b\u043e \\(w=1\\) \u043a\u0430\u043a \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u043e\u0435 \u0432 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u043e\u0440\u043c\u0435. \\(w=1+0\\cdot i\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0417\u0434\u0435\u0441\u044c \\(a=1,\\ b=0\\). \\(|w|=1, \\ \\phi=0\\).  <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u043e\u0433\u0434\u0430  \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \\(z=\\sqrt[6]{1}\\) \u0438\u043c\u0435\u0435\u0442 6 \u043a\u043e\u0440\u043d\u0435\u0439:  <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(z_k=\\sqrt[6]{|1|}(\\cos {\\frac{2\\pi k}{6}}+i\\ \\sin {\\frac{2\\pi k}{6}})\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(z_0=\\cos  0+i\\ \\sin 0=1\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(z_1=\\cos {\\frac{2\\pi }{6}}+i\\ \\sin {\\frac{2\\pi }{6}}=cos {\\frac{\\pi }{3}}+i\\ \\sin {\\frac{\\pi }{3}}=\\frac{1}{2}+\\frac{\\sqrt{3}}{2}i\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(z_2=\\cos {\\frac{2\\pi \\cdot 2}{6}}+i\\ \\sin {\\frac{2\\pi \\cdot 2}{6}}=\\cos {\\frac{2\\pi }{3}}+i\\ \\sin {\\frac{2\\pi }{3}}=-\\frac{1}{2}+\\frac{\\sqrt{3}}{2}i\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(z_3=\\cos {\\frac{2\\pi \\cdot 3}{6}}+i\\ \\sin {\\frac{2\\pi \\cdot 3}{6}}=\\cos {\\pi}+i\\ \\sin {\\pi}=-1\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(z_4=\\cos {\\frac{2\\pi \\cdot 4}{6}}+i\\ \\sin {\\frac{2\\pi \\cdot 4}{6}}=\\cos {\\frac{4\\pi }{3}}+i\\ \\sin {\\frac{4\\pi }{3}}=-\\frac{1}{2}-\\frac{\\sqrt{3}}{2}i\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(z_5=\\cos {\\frac{2\\pi \\cdot 5}{6}}+i\\ \\sin {\\frac{2\\pi \\cdot 5}{6}}=\\cos {\\frac{5\\pi }{3}}+i\\ \\sin {\\frac{5\\pi }{3}}=\\frac{1}{2}-\\frac{\\sqrt{3}}{2}i\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0417\u0430\u043c\u0435\u0442\u0438\u043c, \u0447\u0442\u043e \u043d\u0438 \u043e\u0434\u043d\u043e \u0438\u0437 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435  \\(z_k\\)  \u043d\u0435 \u0440\u0430\u0432\u043d\u043e \u043d\u0443\u043b\u044e, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0432\u0442\u043e\u0440\u043e\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u0435 \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u044e, \u0437\u0430\u0434\u0430\u043d\u043d\u043e\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0434\u043e\u043b\u0436\u043d\u043e \u0431\u044b\u0442\u044c \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043e \u0442\u043e\u0447\u043a\u043e\u0439, \u0440\u0430\u0441\u043f\u043e\u043b\u043e\u0436\u0435\u043d\u043d\u043e\u0439 \u0432 \u0447\u0435\u0442\u0432\u0435\u0440\u0442\u043e\u043c \u043a\u0432\u0430\u0434\u0440\u0430\u043d\u0442\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0413\u0430\u0443\u0441\u0441\u0430, \u0442\u043e \u0435\u0441\u0442\u044c \\(a&gt;0, \\ b&lt;0\\). \u042d\u0442\u043e\u043c\u0443 \u0443\u0441\u043b\u043e\u0432\u0438\u044e \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u0435\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \\(z_5=\\frac{1}{2}-\\frac{\\sqrt{3}}{2}i\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041e\u0442\u0432\u0435\u0442: \\(z_0=\\frac{1}{2}-\\frac{\\sqrt{3}}{2}i\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\"><strong>(<\/strong><\/mark><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\u05d1)<\/mark><\/strong> \u0414\u0430\u043d \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440 \\(d>0\\). \u0422\u043e\u0447\u043a\u0430 \\(A\\) \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0432 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0413\u0430\u0443\u0441\u0441\u0430 \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \\(d\\cdot z_0=\\frac{d}{2}-\\frac{\\sqrt{3}d}{2}i\\), \u0442\u043e \u0435\u0441\u0442\u044c \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0442\u043e\u0447\u043a\u0438 \\(A(\\frac{d}{2},-\\frac{\\sqrt{3}d}{2})\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u043e\u0447\u043a\u0430 \\(B\\) \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0432 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0413\u0430\u0443\u0441\u0441\u0430 \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \\(d\\cdot z_0\\cdot i=\\frac{d}{2}i-\\frac{\\sqrt{3}d}{2}i\\cdot i=\\frac{\\sqrt{3}d}{2}+\\frac{d}{2}i\\), \u0442\u043e \u0435\u0441\u0442\u044c \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0442\u043e\u0447\u043a\u0438 \\(B(\\frac{\\sqrt{3}d}{2},\\frac{d}{2})\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u043e\u0447\u043a\u0430 \\(C\\) \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0432 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0413\u0430\u0443\u0441\u0441\u0430 \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \\(d\\cdot (z_0)^4\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0427\u0442\u043e\u0431\u044b \u0432\u043e\u0437\u0432\u0435\u0441\u0442\u0438 \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e, \u0437\u0430\u043f\u0438\u0441\u0430\u043d\u043d\u043e\u0435 \u0432 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u043e\u0440\u043c\u0435  \u0432 \u0441\u0442\u0435\u043f\u0435\u043d\u044c \\(n\\in N \\), \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442 \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u041c\u0443\u0430\u0432\u0440\u0430: \u0435\u0441\u043b\u0438 \\(z=|z|(\\cos \\phi+i\\ \\sin \\phi)\\), \u0442\u043e<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"> <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\\(z^n=|z|^n(\\cos (n\\cdot \\phi)+i\\ \\sin (n\\cdot \\phi))\\)<\/mark>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0412\u043e\u0437\u0432\u0435\u0434\u0435\u043c \u0447\u0438\u0441\u043b\u043e \\(z_0=1 \\cdot (\\cos {\\frac{5\\pi }{3}}+i\\ \\sin {\\frac{5 \\pi }{3}}) \\) \u0432 \u0447\u0435\u0442\u0432\u0435\u0440\u0442\u0443\u044e \u0441\u0442\u0435\u043f\u0435\u043d\u044c. \u041f\u043e\u043b\u0443\u0447\u0438\u043c <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(z_0^4=1^4\\cdot (\\cos (4\\cdot{\\frac{5\\pi }{3}})+i\\ \\sin (4\\cdot{\\frac{5\\pi }{3}}))=\\cos {\\frac{20\\pi }{3}}+i\\ \\sin {\\frac{20\\pi }{3}}=\\cos (6\\pi+\\frac{2\\pi }{3})+i\\ \\sin (6\\pi+\\frac{2\\pi }{3})\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(= -\\frac{1}{2}+\\frac{\\sqrt{3}}{2} i \\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041e\u0442\u0441\u044e\u0434\u0430 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0442\u043e\u0447\u043a\u0438 \\(C(-\\frac{d}{2}, \\frac{\\sqrt{3}d}{2} i )\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u043e\u0447\u043a\u0438 \\(A(\\frac{d}{2},\\frac{\\sqrt{3}d}{2})\\), \\(B(\\frac{\\sqrt{3}d}{2},\\frac{d}{2})\\) \u0438 \\(C(-\\frac{d}{2}, \\frac{\\sqrt{3}d}{2} i )\\) \u043b\u0435\u0436\u0430\u0442 \u043d\u0430 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438 \u0440\u0430\u0434\u0438\u0443\u0441\u0430 \\(d\\), \u0442\u0430\u043a \u043a\u0430\u043a \u043c\u043e\u0434\u0443\u043b\u0438 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u0445 \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b \u0440\u0430\u0432\u043d\u044b \\(d\\). <\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u0418\u0437\u0432\u0435\u0441\u0442\u043d\u043e, \u0447\u0442\u043e \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \\(ABC\\) \u0440\u0430\u0432\u043d\u0430  \\(5d+6\\). \u041d\u0430\u0439\u0434\u0435\u043c \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443 \\(d\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(OA=OB=OC=d\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0414\u043e\u043a\u0430\u0436\u0435\u043c, \u0447\u0442\u043e \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0438 \\(AOB\\) \u0438 \\(COB\\) &#8212; \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u044b\u0435. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0434\u043e\u043a\u0430\u0436\u0435\u043c, \u0447\u0442\u043e \\(\\overrightarrow{ OA}\\perp \\overrightarrow{ OB}\\),  \\(\\overrightarrow{ OC}\\perp \\overrightarrow{ OB}\\).  \u0412\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b, \u0435\u0441\u043b\u0438 \u0438\u0445 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0440\u0430\u0432\u043d\u043e \u043d\u0443\u043b\u044e. \u0421\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0440\u0430\u0432\u043d\u043e \u0441\u0443\u043c\u043c\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0439 \u043e\u0434\u043d\u043e\u0438\u043c\u0435\u043d\u043d\u044b\u0445 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\overrightarrow{ OA}\\cdot \\overrightarrow{ OB}=\\frac{d}{2}\\cdot \\frac{\\sqrt{3}d}{2}+(- \\frac{\\sqrt{3}d}{2})\\cdot \\frac{d}{2}=0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\overrightarrow{ O\u0421}\\cdot \\overrightarrow{ OB}=(-\\frac{d}{2})\\cdot \\frac{\\sqrt{3}d}{2}+\\frac{\\sqrt{3}d}{2})\\cdot \\frac{d}{2}=0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0438 \\(AOB\\) \u0438 \\(COB\\) &#8212; \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u044b\u0435. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0417\u0430\u043c\u0435\u0442\u0438\u043c, \u0447\u0442\u043e \u043c\u043e\u0436\u043d\u043e \u0431\u044b\u043b\u043e \u043d\u0430\u0439\u0442\u0438 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u044b \u0432 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0437\u0430\u043f\u0438\u0441\u0438 \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b, \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u043c \u0442\u043e\u0447\u043a\u0430\u043c \\(A, \\ B,\\ C\\) \u0438 \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u044c, \u0447\u0442\u043e \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0438 \\(AOB\\) \u0438 \\(COB\\) \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u044b\u0435, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0443\u0433\u043b\u044b. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0418\u0442\u0430\u043a, \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u0438, \u0447\u0442\u043e  \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430  \\(ABC\\) \u0440\u0430\u0432\u043d\u0430 \u0441\u0443\u043c\u043c\u0435 \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439 \u0434\u0432\u0443\u0445 \u0440\u0430\u0432\u043d\u044b\u0445 \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u044b\u0445 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u043e\u0432 \\(COB\\) \u0438 \\(AOB\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(S_\\Delta {COB}=S_\\Delta {AOB}=\\frac{d\\cdot d}{2}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(S_\\Delta {ABC}=2\\cdot \\frac{d\\cdot d}{2}=d^2=5d+6\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0420\u0435\u0448\u0438\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435: \\(d^2-5d-6=0\\). \\(d_1=6, \\ d_2=-1\\). \u041f\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u044e \\(d&gt;0\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u041e\u0442\u0432\u0435\u0442<\/em>: 6<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-8 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"714\" height=\"670\" data-id=\"873\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/76-1.png\" alt=\"\" class=\"wp-image-873\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/76-1.png 714w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/76-1-300x282.png 300w\" sizes=\"auto, (max-width: 714px) 100vw, 714px\" \/><\/figure>\n<\/figure>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-9 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"712\" height=\"646\" data-id=\"877\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/77.png\" alt=\"\" class=\"wp-image-877\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/77.png 712w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/77-300x272.png 300w\" sizes=\"auto, (max-width: 712px) 100vw, 712px\" \/><\/figure>\n<\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\"><strong>(<\/strong><\/mark><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\u05d2)<\/mark><\/strong> \\(w= ((z_0)^2-\\frac{1}{(z_0)^2})(1+i)\\). \u041d\u0430\u0439\u0434\u0435\u043c \\(|w|\\) \u0438 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442 \\(w\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \\(((z_0)^2-\\frac{1}{(z_0)^2})(1+i)\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(z_0=\\frac{1}{2}-\\frac{\\sqrt{3}}{2}i\\) (\u0438\u0437 \u043f. <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\"><strong>(<\/strong><\/mark><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\u05d0)<\/mark><\/strong>)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(z_0^2=(\\frac{1}{2}-\\frac{\\sqrt{3}}{2}i)^2=\\frac{1}{4}-2\\cdot \\frac{1}{2}\\cdot\\frac{\\sqrt{3}}{2}i+(\\frac{\\sqrt{3}}{2}i)^2=\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(=\\frac{1}{4}-\\frac{\\sqrt{3}}{2}i-\\frac{3}{4}=-\\frac{1}{2}-\\frac{\\sqrt{3}}{2}i\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\frac{1}{z_0^2}=\\frac{1}{-\\frac{1}{2}-\\frac{\\sqrt{3}}{2}i}=-\\frac{1}{\\frac{1}{2}+\\frac{\\sqrt{3}}{2}i}=\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(=-\\frac{\\frac{1}{2}-\\frac{\\sqrt{3}}{2}i}{(\\frac{1}{2}+\\frac{\\sqrt{3}}{2}i)(\\frac{1}{2}-\\frac{\\sqrt{3}}{2}i)}=\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(=-\\frac{\\frac{1}{2}-\\frac{\\sqrt{3}}{2}i}{\\frac{1}{4}+\\frac{3}{4}}=-\\frac{1}{2}+\\frac{\\sqrt{3}}{2}i\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0417\u0430\u043c\u0435\u0447\u0430\u043d\u0438\u0435: \\(z_0^2\\) \u0438 \\(\\frac{1}{z_0^2}\\) \u043c\u043e\u0436\u043d\u043e \u0431\u044b\u043b\u043e \u043d\u0430\u0439\u0442\u0438, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0444\u043e\u0440\u043c\u0443 \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430 \\(z_0\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(z_0^2-\\frac{1}{z_0^2}=-\\frac{1}{2}-\\frac{\\sqrt{3}}{2}i +\\frac{1}{2}-\\frac{\\sqrt{3}}{2}i=-\\sqrt{3}i\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(w=(-\\sqrt{3}i)(1+i)=-\\sqrt{3}i+\\sqrt{3}=\\sqrt{3} -i\\sqrt{3} \\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(a=\\sqrt{3}&gt;0,\\ b=-\\sqrt{3}&lt;0\\), \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0442\u043e\u0447\u043a\u0430 \u0440\u0430\u0441\u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0430 \u0432 4 \u043a\u0432\u0430\u0434\u0440\u0430\u043d\u0442\u0435. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(|w|=\\sqrt{(\\sqrt{3})^2+(-\\sqrt{3})^2}=\\sqrt{6}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(arg (w)=arctg\\frac{\\sqrt{3}}{-\\sqrt{3}}=arctg(-1)\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0410\u0440\u0433\u0443\u043c\u0435\u043d\u0442 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0437\u0430\u043f\u0438\u0441\u0430\u0442\u044c \u0432 \u043b\u044e\u0431\u043e\u043c \u0432\u0438\u0434\u0435, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \\(\\alpha=-45^{\\circ}\\) \u0438\u043b\u0438 \\(\\alpha=315^{\\circ}\\) \u0438\u043b\u0438 \\(\\alpha=-\\frac{\\pi}{4}\\) \u0438\u043b\u0438 \\(\\alpha=\\frac{7\\pi}{4}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041e\u0442\u0432\u0435\u0442: \\(|w|=\\sqrt{6}\\), \\(\\alpha=315^{\\circ}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\"><strong>(<\/strong><\/mark><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\u05d3)<\/mark><\/strong> \u0414\u0430\u043d\u043e, \u0447\u0442\u043e \\(w^n\\) &#8212;  \u0447\u0438\u0441\u0442\u043e \u043c\u043d\u0438\u043c\u043e\u0435 \u0447\u0438\u0441\u043b\u043e, \u0440\u0430\u0441\u043f\u043e\u043b\u043e\u0436\u0435\u043d\u043d\u043e\u0435 \u0437\u0430 \u043f\u0440\u0435\u0434\u0435\u043b\u0430\u043c\u0438 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438, \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u044e\u0449\u0435\u0439 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a  \\(ABC\\). \u041d\u0443\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \\(n\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0417\u0430\u043f\u0438\u0448\u0435\u043c \u0447\u0438\u0441\u043b\u043e \\(w= \\sqrt{3} -i\\sqrt{3} \\) \u0432 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u043e\u0440\u043c\u0435.  \u0423\u0447\u0438\u0442\u044b\u0432\u0430\u044f \u043f. <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\"><strong>(<\/strong><\/mark><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\u05d2)<\/mark><\/strong> \u043f\u043e\u043b\u0443\u0447\u0438\u043c:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(w=\\sqrt{6}(\\cos(315^{\\circ}) +i\\sin (315^{\\circ}) \\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \u041c\u0443\u0430\u0432\u0440\u0430: \\(w^n=\\sqrt{6}^n(\\cos(315^{\\circ}\\cdot n) +i\\sin (315^{\\circ}\\cdot n) \\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(w^n\\) &#8212; \u0447\u0438\u0441\u0442\u043e \u043c\u043d\u0438\u043c\u043e\u0435 \u0447\u0438\u0441\u043b\u043e, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \\(\\cos(315^{\\circ}\\cdot n)=0\\). \u042d\u0442\u043e \u0437\u043d\u0430\u0447\u0438\u0442, \u0447\u0442\u043e \\(315^{\\circ}\\cdot n\\) \u0434\u043e\u043b\u0436\u043d\u043e \u0431\u044b\u0442\u044c \u043a\u0440\u0430\u0442\u043d\u043e \\(90^{\\circ}\\). \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u044d\u0442\u043e \u0447\u0438\u0441\u043b\u043e \u0440\u0430\u0441\u043f\u043e\u043b\u043e\u0436\u0435\u043d\u043e \u0437\u0430 \u043f\u0440\u0435\u0434\u0435\u043b\u0430\u043c\u0438 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438, \u0440\u0430\u0434\u0438\u0443\u0441 \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0440\u0430\u0432\u0435\u043d 6 (\\(d=6 \\) \u0438\u0437 \u043f. <strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(\u05d1)<\/mark><\/strong>. \u0417\u043d\u0430\u0447\u0438\u0442, \\(|w^n|&gt;6\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041d\u0430\u0439\u0434\u0435\u043c \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0435\u0435 \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \\(\\sqrt{6}^n&gt;6\\): \\(n=3\\). \u0414\u043b\u044f \u0442\u043e\u0433\u043e, \u0447\u0442\u043e\u0431\u044b \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c \u0447\u0435\u043c\u0443 \u0440\u0430\u0432\u0435\u043d  \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u043f\u0440\u0438 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u0445 \\(n\\ge 3\\), \u043d\u0430\u043c \u0443\u0434\u043e\u0431\u043d\u0435\u0435 \u0432\u0437\u044f\u0442\u044c \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442 \u0440\u0430\u0432\u043d\u044b\u043c \\(-\\frac{\\pi}{4}\\):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(n=3: \\ \\cos (-\\frac{\\pi}{4}\\cdot 3)=-\\frac {\\sqrt{2}}{2}\\ne 0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(n=4: \\ \\cos (-\\frac{\\pi}{4}\\cdot 4)=-1\\ne 0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(n=5: \\ \\cos (-\\frac{\\pi}{4}\\cdot 5)=-\\frac {\\sqrt{2}}{2}\\ne 0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(n=6: \\ \\cos (-\\frac{\\pi}{4}\\cdot 6)=\\cos (-\\frac{3\\pi}{2})=0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u041e\u0442\u0432\u0435\u0442:<\/em> 6<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/div>\n\t\t\t<\/div><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0438\u0441\u0442\u043e\u0447\u043d\u0438\u043a<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[],"class_list":["post-790","post","type-post","status-publish","format-standard","hentry","category-13"],"_links":{"self":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/790","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=790"}],"version-history":[{"count":123,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/790\/revisions"}],"predecessor-version":[{"id":1315,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/790\/revisions\/1315"}],"wp:attachment":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=790"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=790"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=790"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}