{"id":816,"date":"2016-09-02T12:47:22","date_gmt":"2016-09-02T17:47:22","guid":{"rendered":"http:\/\/naps.com.mx\/blog\/?p=816"},"modified":"2017-11-16T12:13:44","modified_gmt":"2017-11-16T18:13:44","slug":"potencias-de-i","status":"publish","type":"post","link":"https:\/\/naps.com.mx\/blog\/potencias-de-i\/","title":{"rendered":"Potencias de i"},"content":{"rendered":"<p>Se muestra c\u00f3mo calcular <span class=\"wp-katex-eq\" data-display=\"false\">i <\/span> (unidad imaginaria) elevada a cualquier potencia.<\/p>\n<div id=\"attachment_836\" style=\"width: 900px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/naps.com.mx\/blog\/wp-content\/uploads\/2016\/09\/potencias-de-i.jpeg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-836\" class=\"size-full wp-image-836\" src=\"http:\/\/naps.com.mx\/blog\/wp-content\/uploads\/2016\/09\/potencias-de-i.jpeg\" alt=\"Potencias de i\" width=\"890\" height=\"593\" srcset=\"https:\/\/naps.com.mx\/blog\/wp-content\/uploads\/2016\/09\/potencias-de-i.jpeg 890w, https:\/\/naps.com.mx\/blog\/wp-content\/uploads\/2016\/09\/potencias-de-i-300x200.jpeg 300w\" sizes=\"auto, (max-width: 890px) 100vw, 890px\" \/><\/a><p id=\"caption-attachment-836\" class=\"wp-caption-text\">Aprende m\u00e1s sobre potencias de i (unidad imaginaria)<\/p><\/div>\n<p><!--more--><\/p>\n<p>Un n\u00famero complejo es aquel formado por una parte real y una parte imaginaria. La unidad imaginaria se denomina <span class=\"wp-katex-eq\" data-display=\"false\">i <\/span>\u00a0y tiene el valor de <span class=\"wp-katex-eq\" data-display=\"false\"> \\sqrt{-1} <\/span>. Por lo que <span class=\"wp-katex-eq\" data-display=\"false\">i^2=-1<\/span>.<\/p>\n<p>Entonces las primeras potencias de <span class=\"wp-katex-eq\" data-display=\"false\">i<\/span> ser\u00edan:<\/p>\n<ul>\n<li><span class=\"wp-katex-eq\" data-display=\"false\">i^0=1<\/span>, pues todo n\u00famero elevado a la 0 es 1.<\/li>\n<li><span class=\"wp-katex-eq\" data-display=\"false\">i^1=i<\/span>, pues todo n\u00famero elevado a la 1 es el mismo n\u00famero<\/li>\n<li><span class=\"wp-katex-eq\" data-display=\"false\">i^2=-1<\/span>, por la raz\u00f3n que se explica en el primer p\u00e1rrafo de este art\u00edculo.<\/li>\n<li><span class=\"wp-katex-eq\" data-display=\"false\">i^3=-i<\/span>, porque\u00a0<span class=\"wp-katex-eq\" data-display=\"false\">i^3=i^2*i^1=i*(-1)=-i<\/span><\/li>\n<\/ul>\n<p>Como te puedes dar cuenta, las siguientes potencias volver\u00edan a repetirse constantemente.<\/p>\n<p>Una forma de calcular potencias grandes es observando el residuo de la divisi\u00f3n por 4 de la potencia a calcular.\u00a0Por ejemplo,\u00a0<span class=\"wp-katex-eq\" data-display=\"false\">i^4=1 <\/span>\u00a0porque <span class=\"wp-katex-eq\" data-display=\"false\">i^4=i^3*i^1=-i*i=-i^2=-(-1)=1<\/span>.<\/p>\n<p>Pero otra forma de calcular <span class=\"wp-katex-eq\" data-display=\"false\">i^4<\/span> es dividiendo 4 (la potencia buscada) entre 4 y observando el residuo de la divisi\u00f3n. El residuo es 0. Por lo que<\/p>\n<span class=\"wp-katex-eq\" data-display=\"false\">i^4=i^0=1<\/span>\n<p>Entonces, si se requiere calcular <span class=\"wp-katex-eq\" data-display=\"false\">i^{315}<\/span> dividimos 315 entre 4 y observamos el residuo de la divisi\u00f3n que es 3, por lo que<\/p>\n<span class=\"wp-katex-eq\" data-display=\"false\">i^{315}=i^3=-i<\/span>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Se muestra c\u00f3mo calcular (unidad imaginaria) elevada a cualquier potencia.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"amp_status":"","footnotes":""},"categories":[164],"tags":[165,177],"class_list":["post-816","post","type-post","status-publish","format-standard","hentry","category-algebra-lineal","tag-numeros-complejos","tag-potencias-de-i"],"_links":{"self":[{"href":"https:\/\/naps.com.mx\/blog\/wp-json\/wp\/v2\/posts\/816","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/naps.com.mx\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/naps.com.mx\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/naps.com.mx\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/naps.com.mx\/blog\/wp-json\/wp\/v2\/comments?post=816"}],"version-history":[{"count":20,"href":"https:\/\/naps.com.mx\/blog\/wp-json\/wp\/v2\/posts\/816\/revisions"}],"predecessor-version":[{"id":837,"href":"https:\/\/naps.com.mx\/blog\/wp-json\/wp\/v2\/posts\/816\/revisions\/837"}],"wp:attachment":[{"href":"https:\/\/naps.com.mx\/blog\/wp-json\/wp\/v2\/media?parent=816"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/naps.com.mx\/blog\/wp-json\/wp\/v2\/categories?post=816"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/naps.com.mx\/blog\/wp-json\/wp\/v2\/tags?post=816"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}