{"id":1158,"date":"2010-07-26T17:33:00","date_gmt":"2010-07-26T15:33:00","guid":{"rendered":"http:\/\/matematicas.jesussoto.es\/?p=1158"},"modified":"2013-01-27T15:38:40","modified_gmt":"2013-01-27T15:38:40","slug":"los-recursos-de-la-formula-de-de-moivre","status":"publish","type":"post","link":"http:\/\/pimedios.jesussoto.es\/?p=1158","title":{"rendered":"Los recursos de la f\u00f3rmula de De Moivre"},"content":{"rendered":"<p>Ahora que se nos echa encima el periodo de vacaciones no est&aacute; mal recordar algunas f&oacute;rmulas, que nos ayudan a resolver ejercicios, que peri&oacute;dicamente aparecen en nuestros estudios.<\/p>\n<p>Una de ellas es la f&oacute;rmula de De Moivre y un ejemplo cl&aacute;sico es su utilizaci&oacute;n para expresar m&uacute;ltiplos del coseno o del seno, ve&aacute;moslo con&nbsp; el cos(5<em>&theta;<\/em>) en funci&oacute;n del cos(<em>&theta;<\/em>) y el sin(5<em>&theta;<\/em>) en funci&oacute;n del sin(<em>&theta;<\/em>).<\/p>\n<p>Apliquemos la f&oacute;rmula y desarrollemos el binomio mediante la f&oacute;rmula del binomio de Newton:<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" width=\"401\" height=\"79\" alt=\"\" src=\"http:\/\/pimedios.es\/wp-content\/uploads\/moivre1.png\" \/><\/p>\n<p style=\"text-align: right;\"><img loading=\"lazy\" decoding=\"async\" width=\"315\" height=\"48\" alt=\"\" src=\"http:\/\/pimedios.es\/wp-content\/uploads\/moivre2.png\" \/><\/p>\n<p style=\"text-align: right;\"><img loading=\"lazy\" decoding=\"async\" width=\"269\" height=\"52\" alt=\"\" src=\"http:\/\/pimedios.es\/wp-content\/uploads\/moivre3.png\" \/><\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" width=\"331\" height=\"38\" alt=\"\" src=\"http:\/\/pimedios.es\/wp-content\/uploads\/moivre4.png\" \/><\/p>\n<p style=\"text-align: right;\"><img loading=\"lazy\" decoding=\"async\" width=\"332\" height=\"26\" alt=\"\" src=\"http:\/\/pimedios.es\/wp-content\/uploads\/moivre5.png\" \/><\/p>\n<p style=\"text-align: left;\">Igualando parte real y parte imaginaria tendremos<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" width=\"386\" height=\"59\" alt=\"\" src=\"http:\/\/pimedios.es\/wp-content\/uploads\/moivre6.png\" \/><\/p>\n<p>Para dejarlo s&oacute;lo con t&eacute;rminos de cosenos y senos es suficiente con recordar que<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" width=\"140\" height=\"29\" alt=\"\" src=\"http:\/\/pimedios.es\/wp-content\/uploads\/moivre7.png\" \/><\/p>\n<p>y por tanto,<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" width=\"460\" height=\"142\" src=\"http:\/\/pimedios.es\/wp-content\/uploads\/moivre8.png\" alt=\"\" \/><\/p>\n<p>&nbsp;<\/p>\n<h3>Enlaces de inter&eacute;s:<\/h3>\n<ul>\n<li><a href=\"http:\/\/pimedios.es\/?p=880\">La f&oacute;rmula de De Moivre<\/a>,<\/li>\n<li><a href=\"http:\/\/es.wikipedia.org\/wiki\/F%C3%B3rmula_de_De_Moivre\">F&oacute;rmula de De Moivre<\/a>, wikipedia<\/li>\n<li><a href=\"http:\/\/www.youtube.com\/watch?v=LS6y8hOUPwY\">Potencia de un n&uacute;mero complejo por la f&oacute;rmula de Moivre<\/a>, juanmemol, video<\/li>\n<li><a href=\"http:\/\/www.youtube.com\/watch?v=h2DwafPkems&amp;feature=related\">M&uacute;ltiplos de &aacute;ngulos y f&oacute;rmula de Moivre<\/a>, juanmemol, video<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ahora que se nos echa encima el periodo de vacaciones no est&aacute; mal recordar algunas f&oacute;rmulas, que nos ayudan a resolver ejercicios, que peri&oacute;dicamente aparecen en nuestros estudios. Una de ellas es la f&oacute;rmula de De Moivre y un ejemplo cl&aacute;sico es su utilizaci&oacute;n para expresar m&uacute;ltiplos del coseno o del seno, ve&aacute;moslo con&nbsp; el&hellip; <a class=\"more-link\" href=\"http:\/\/pimedios.jesussoto.es\/?p=1158\">Seguir leyendo <span class=\"screen-reader-text\">Los recursos de la f\u00f3rmula de De Moivre<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[80,262],"class_list":["post-1158","post","type-post","status-publish","format-standard","hentry","category-ocio","tag-complejos","tag-moivre","entry"],"_links":{"self":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/1158","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1158"}],"version-history":[{"count":2,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/1158\/revisions"}],"predecessor-version":[{"id":3654,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/1158\/revisions\/3654"}],"wp:attachment":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1158"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1158"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1158"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}