{"id":1172,"date":"2010-07-27T10:14:38","date_gmt":"2010-07-27T08:14:38","guid":{"rendered":"http:\/\/matematicas.jesussoto.es\/?p=1172"},"modified":"2010-07-27T10:14:38","modified_gmt":"2010-07-27T08:14:38","slug":"potencia-de-un-complejo-usando-de-moivre","status":"publish","type":"post","link":"http:\/\/pimedios.jesussoto.es\/?p=1172","title":{"rendered":"Potencia de un complejo usando De Moivre"},"content":{"rendered":"<p>&nbsp;<\/p>\n<p>Continuando con ejemplos de ejercicios y visto que ayer utilizamos la f&oacute;rmula de Moivre, os propongo otro uso habitual de esta f&oacute;rmula: el c&aacute;lculo de potencias de complejos.<\/p>\n<p>Por ejemplo, calculemos (5+7<em>i<\/em>)<sup>11<\/sup>. Primero recordemos que<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" width=\"285\" height=\"70\" alt=\"\" src=\"http:\/\/matematicas.jesussoto.es\/wp-content\/uploads\/moivre9.png\" \/><\/p>\n<p>Luego<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" width=\"450\" height=\"62\" src=\"http:\/\/matematicas.jesussoto.es\/wp-content\/uploads\/moivre10.png\" alt=\"\" \/><\/p>\n<p>El arctan(5,7) designa el arcotangente del punto (5,7) en el plano complejo cartesiano, cuyo valor ser&aacute; &pi;\/6. Sustituimos para obtener el resultado:<\/p>\n<p style=\"text-align: center;\">$ (5+i7)^{11}=74^5\\sqrt{74}(\\cos(11\\frac{\\pi}{6})+i\\sin(11\\frac{\\pi}{6}))$<\/p>\n<p>&nbsp;<\/p>\n<h3>Enlaces de inter&eacute;s:<\/h3>\n<ul>\n<li><a href=\"http:\/\/matematicas.jesussoto.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<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp; Continuando con ejemplos de ejercicios y visto que ayer utilizamos la f&oacute;rmula de Moivre, os propongo otro uso habitual de esta f&oacute;rmula: el c&aacute;lculo de potencias de complejos. Por ejemplo, calculemos (5+7i)11. Primero recordemos que Luego El arctan(5,7) designa el arcotangente del punto (5,7) en el plano complejo cartesiano, cuyo valor ser&aacute; &pi;\/6. Sustituimos&hellip; <a class=\"more-link\" href=\"http:\/\/pimedios.jesussoto.es\/?p=1172\">Seguir leyendo <span class=\"screen-reader-text\">Potencia de un complejo usando 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-1172","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\/1172","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=1172"}],"version-history":[{"count":0,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/1172\/revisions"}],"wp:attachment":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1172"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1172"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1172"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}