{"id":24032,"date":"2021-12-16T19:56:53","date_gmt":"2021-12-16T14:26:53","guid":{"rendered":"https:\/\/yanamtakshashila.com\/?p=24032"},"modified":"2022-02-04T19:45:49","modified_gmt":"2022-02-04T14:15:49","slug":"de-movires-theorem-revision","status":"publish","type":"post","link":"https:\/\/yanamtakshashila.com\/?p=24032","title":{"rendered":"DE-MOVIRE&#8217;S THEOREM (REVISION)"},"content":{"rendered":"\n<script async=\"\" src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-9453835310745500\" crossorigin=\"anonymous\"><\/script>\n<!-- Leader board 1 -->\n<ins class=\"adsbygoogle\" style=\"display:inline-block;width:728px;height:90px\" data-ad-client=\"ca-pub-9453835310745500\" data-ad-slot=\"8769628924\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[1.\\ Prove\\ that:\\  [\\frac{cos\u2061\\  \u03b8 +  i sin\u2061\\  \u03b8} {sin\u2061\\  \u03b8 &#8211;  i cos\\  \u03b8}]^4\\ = 1\\ \\hspace{18cm}\\]<script src=\"https:\/\/yanamtakshashila.com\/wp-includes\/js\/dist\/hooks.min.js?ver=dd5603f07f9220ed27f1\" id=\"wp-hooks-js\"><\/script>\n<script src=\"https:\/\/yanamtakshashila.com\/wp-includes\/js\/dist\/i18n.min.js?ver=c26c3dc7bed366793375\" id=\"wp-i18n-js\"><\/script>\n<script id=\"wp-i18n-js-after\">\nwp.i18n.setLocaleData( { 'text direction\\u0004ltr': [ 'ltr' ] } );\n\/\/# sourceURL=wp-i18n-js-after\n<\/script>\n<script  async src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-MML-AM_CHTML\" id=\"mathjax-js\"><\/script>\n<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color {black}{Solution:}\\  Question\\ No.\\  8\\ Solution\\ \\hspace{2cm}\\]<\/div>\n\n\n\n<p><a href=\"https:\/\/yanamtakshashila.com\/2021\/10\/13\/unit-ii-complex-numbers-2\/\">https:\/\/yanamtakshashila.com\/2021\/10\/13\/unit-ii-complex-numbers-2\/<\/a><\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[2:\\ Simplify\\ using\\ DeMoivre\u2019s\\ theorem:\\ \\frac{(cos\u2061\\  2\u03b8 &#8211;  i sin\u2061\\  2\u03b8)^7\\ (cos\u2061\\  3\u03b8 +  i sin\u2061\\  3\u03b8)^{-5}} {(cos\u2061\\  4\u03b8 + i sin\u2061\\  4\u03b8)^2\\ (cos\u2061\\  5\u03b8 &#8211;  i sin\u2061\\  5\u03b8)^{-6}}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color {black}{Solution:}\\ \\frac{(cos\u2061\\  2\u03b8 &#8211;  i sin\u2061\\  2\u03b8)^7\\ (cos\u2061\\  3\u03b8 +  i sin\u2061\\  3\u03b8)^{-5}} {(cos\u2061\\  4\u03b8 + i sin\u2061\\  4\u03b8)^2\\ (cos\u2061\\  5\u03b8 &#8211;  i sin\u2061\\  5\u03b8)^{-6}}\\ \\hspace{18cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[= \\frac{(cos\u2061\\  \u03b8 +  i sin\u2061\\  \u03b8)^{7 \\times -2}\\ (cos\u2061\\  \u03b8 +  i sin\u2061\\  \u03b8)^{3 \\times -5}} {(cos\u2061\\  \u03b8 + i sin\u2061\\  \u03b8)^{4 \\times 2}\\ (cos\u2061\\  \u03b8 +  i sin\u2061\\  \u03b8)^{-5 \\times -6 }}\\ \\hspace{8cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\"><\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[= \\frac{(cos\u2061\\  \u03b8 +  i sin\u2061\\  \u03b8)^{-14}\\ (cos\u2061\\  \u03b8 +  i sin\u2061\\  \u03b8)^{-15}} {(cos\u2061\\  \u03b8 + i sin\u2061\\  \u03b8)^{8}\\ (cos\u2061\\  \u03b8 +  i sin\u2061\\  \u03b8)^{30}}\\ \\hspace{8cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[=  (cos\\ \u03b8 +  i sin\u2061\\ \u03b8 )^{-\\ 14\\ -\\ 15\\ -\\ 8\\ -\\ 30}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[=  (cos\\ \u03b8 +  i sin\u2061\\ \u03b8 )^{-67}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[=  cos\\ 67\\ \u03b8\\ -\\  i sin\u2061\\ 67\\ \u03b8\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<script async=\"\" src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-9453835310745500\" 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