{"id":839,"date":"2025-09-01T21:31:20","date_gmt":"2025-09-02T03:31:20","guid":{"rendered":"https:\/\/portal.pronea.gt\/?p=839"},"modified":"2025-09-01T21:44:48","modified_gmt":"2025-09-02T03:44:48","slug":"temporary-title-790-2-2-2-2-2","status":"publish","type":"post","link":"https:\/\/portal.pronea.gt\/?p=839","title":{"rendered":"N\u00fameros complejos: cuando lo real y lo imaginario se encuentran"},"content":{"rendered":"<div id=\"cmsmasters_row_0j6royqael\" class=\"cmsmasters_row cmsmasters_color_scheme_default cmsmasters_row_top_default cmsmasters_row_bot_default cmsmasters_row_boxed\">\n<div class=\"cmsmasters_row_outer_parent\">\n<div class=\"cmsmasters_row_outer\">\n<div class=\"cmsmasters_row_inner\">\n<div class=\"cmsmasters_row_margin\">\n<div id=\"cmsmasters_column_69dy6p9ke\" class=\"cmsmasters_column one_first\">\n<div class=\"cmsmasters_column_inner\"><div class=\"cmsmasters_text\" data-animation=\"fadeInRight\" data-delay=\"0\">\n<p data-start=\"2104\" data-end=\"2424\">En matem\u00e1ticas, siempre buscamos formas de explicar la realidad. Sin embargo, existen problemas que los n\u00fameros que usamos todos los d\u00edas no pueden resolver. Es aqu\u00ed donde aparecen los <strong data-start=\"2289\" data-end=\"2310\">n\u00fameros complejos<\/strong>, una combinaci\u00f3n de lo real y lo imaginario que abre nuevas posibilidades en el aprendizaje y la vida pr\u00e1ctica.<\/p>\n<p data-start=\"2426\" data-end=\"2519\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f3a5.svg\" alt=\"\ud83c\udfa5\" \/> <strong data-start=\"2429\" data-end=\"2451\">Mira el video aqu\u00ed<\/strong><\/p>\n<iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/5NxEx0dPK8g?si=Q20wOnHBHi0X2GYx\" width=\"1120\" height=\"630\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe>\n<hr data-start=\"2521\" data-end=\"2524\" \/>\n<h2 data-start=\"2526\" data-end=\"2565\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f50e.svg\" alt=\"\ud83d\udd0e\" \/> \u00bfQu\u00e9 son los n\u00fameros complejos?<\/h2>\n<p data-start=\"2566\" data-end=\"2619\">Un <strong data-start=\"2569\" data-end=\"2588\">n\u00famero complejo<\/strong> est\u00e1 formado por dos partes:<\/p>\n<ul>\n<li data-start=\"2622\" data-end=\"2685\">Una parte <strong data-start=\"2632\" data-end=\"2640\">real<\/strong> (como los n\u00fameros que usamos normalmente).<\/li>\n<li data-start=\"2688\" data-end=\"2763\">Una parte <strong data-start=\"2698\" data-end=\"2712\">imaginaria<\/strong>, representada con la letra <em data-start=\"2740\" data-end=\"2743\">i<\/em>, donde <em data-start=\"2751\" data-end=\"2760\">i\u00b2 = -1<\/em>.<\/li>\n<\/ul>\n<p data-start=\"2765\" data-end=\"2784\">Ejemplo: <em data-start=\"2774\" data-end=\"2782\">3 + 2i<\/em><\/p>\n<hr data-start=\"2786\" data-end=\"2789\" \/>\n<h2 data-start=\"2791\" data-end=\"2838\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/270d.svg\" alt=\"\u270d\ufe0f\" \/> Representaci\u00f3n de los n\u00fameros complejos<\/h2>\n<p data-start=\"2839\" data-end=\"3040\">Los n\u00fameros complejos no solo se escriben, tambi\u00e9n pueden representarse en un plano llamado <strong data-start=\"2931\" data-end=\"2949\">plano complejo<\/strong>, donde el eje horizontal representa la parte real y el eje vertical la parte imaginaria.<\/p>\n<hr data-start=\"3042\" data-end=\"3045\" \/>\n<h2 data-start=\"3047\" data-end=\"3094\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f30d.svg\" alt=\"\ud83c\udf0d\" \/> \u00bfPara qu\u00e9 sirven los n\u00fameros complejos?<\/h2>\n<p data-start=\"3095\" data-end=\"3151\">Aunque parecen abstractos, tienen muchas aplicaciones:<\/p>\n<ul>\n<li data-start=\"3154\" data-end=\"3219\">En <strong data-start=\"3157\" data-end=\"3181\">ingenier\u00eda el\u00e9ctrica<\/strong>, para analizar corrientes alternas.<\/li>\n<li data-start=\"3222\" data-end=\"3274\">En <strong data-start=\"3225\" data-end=\"3235\">f\u00edsica<\/strong>, para describir ondas y vibraciones.<\/li>\n<li data-start=\"3277\" data-end=\"3352\">En <strong data-start=\"3280\" data-end=\"3294\">tecnolog\u00eda<\/strong>, para el procesamiento de se\u00f1ales y gr\u00e1ficos digitales.<\/li>\n<\/ul>\n<hr data-start=\"3354\" data-end=\"3357\" \/>\n<h2 data-start=\"3359\" data-end=\"3386\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f393.svg\" alt=\"\ud83c\udf93\" \/> Aprender con PRONEA<\/h2>\n<p data-start=\"3387\" data-end=\"3690\">El <strong data-start=\"3390\" data-end=\"3445\">Programa Nacional de Educaci\u00f3n Alternativa \u2013PRONEA\u2013<\/strong> del Ministerio de Educaci\u00f3n de Guatemala brinda la oportunidad a j\u00f3venes y adultos de seguir aprendiendo temas avanzados como los n\u00fameros complejos.<br data-start=\"3594\" data-end=\"3597\" \/>Este conocimiento fortalece la l\u00f3gica, la creatividad y la capacidad de resolver problemas.<\/p>\n<hr data-start=\"3692\" data-end=\"3695\" \/>\n<h2 data-start=\"3697\" data-end=\"3714\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/2705.svg\" alt=\"\u2705\" \/> Conclusi\u00f3n<\/h2>\n<p data-start=\"3715\" data-end=\"3935\">Los <strong data-start=\"3719\" data-end=\"3740\">n\u00fameros complejos<\/strong> son la uni\u00f3n de lo real y lo imaginario para explicar lo que antes parec\u00eda imposible.<br data-start=\"3826\" data-end=\"3829\" \/>Aprenderlos te permite ampliar tu visi\u00f3n de las matem\u00e1ticas y descubrir aplicaciones en la vida moderna.<\/p>\n<p data-start=\"3937\" data-end=\"3988\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f449.svg\" alt=\"\ud83d\udc49\" \/> <strong data-start=\"3940\" data-end=\"3986\">PRONEA: La educaci\u00f3n que transforma vidas.<\/strong><\/p>\n<\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":842,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"image","meta":{"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"footnotes":""},"categories":[33,39],"tags":[],"class_list":["post-839","post","type-post","status-publish","format-image","has-post-thumbnail","hentry","category-matematicas","category-recursos","post_format-post-format-image"],"_links":{"self":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/839","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=839"}],"version-history":[{"count":6,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/839\/revisions"}],"predecessor-version":[{"id":846,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/839\/revisions\/846"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/media\/842"}],"wp:attachment":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=839"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=839"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=839"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}