{"id":114792,"date":"2020-01-29T18:19:56","date_gmt":"2020-01-29T17:19:56","guid":{"rendered":"https:\/\/www.superprof.es\/diccionario\/aritmetica\/multiplicacion-complejos.html"},"modified":"2026-10-07T17:43:45","modified_gmt":"2026-10-07T15:43:45","slug":"multiplicacion-complejos","status":"publish","type":"post","link":"https:\/\/www.superprof.es\/diccionario\/matematicas\/aritmetica\/multiplicacion-complejos.html","title":{"rendered":"Multiplicaci\u00f3n de n\u00fameros complejos"},"content":{"rendered":"<section id=\"sec\" style=\"\">\r\n          \n\n<h3 class=\"wp-block-heading\">Multiplicaci\u00f3n de n\u00fameros complejos en forma bin\u00f3mica<\/h3>\n\n\r\n              \n\n<p class=\"wp-block-paragraph\">El <strong>producto de los n\u00fameros complejos<\/strong> se realiza aplicando la propiedad <strong>distributiva<\/strong> del producto respecto de la suma y teniendo en cuenta que <em><strong>i<\/strong><\/em><strong><sup>2<\/sup> =  \u22121<\/strong>.<\/p>\n\n\r\n              \n\n<p class=\"wp-block-paragraph\"><strong>(a + b<em>i<\/em>)  \u00b7  (c + d<em>i<\/em>) = (ac \u2212 bd) + (ad + bc)<em>i<\/em> <\/strong><\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\">( 5 + 2 <em>i<\/em>)  \u00b7 ( 2  \u2212  3 <em>i<\/em>)  = <\/p>\n\n\r\n\t\t\t\t\t    \n\n<p class=\"wp-block-paragraph\">=10  \u2212 15<em>i<\/em> + 4<em>i<\/em> \u2212 6 <em>i<\/em><sup>2<\/sup> = 10 \u2212 11<em>i<\/em> + 6 = <span class=\"sol\">16 \u2212 11<em>i<\/em><\/span><\/p>\n\n\r\n               \r\n\r\n\t\t\t  \n\n<h3 class=\"wp-block-heading\">Multiplicaci\u00f3n de n\u00fameros complejos en forma polar<\/h3>\n\n\r\n              \n\n<p class=\"wp-block-paragraph\">La <strong>multiplicaci\u00f3n<\/strong>  de dos <strong>n\u00fameros complejos<\/strong> es otro <strong>n\u00famero complejo<\/strong> tal que:<\/p>\n\n\r\n\t\t\t\t\t\t\n\n<p class=\"wp-block-paragraph\">Su m\u00f3dulo es el producto de los m\u00f3dulos.<\/p>\n\n\r\n\t\t\t\t\t\t\t\n\n<p class=\"wp-block-paragraph\">Su argumento es la suma de los argumentos.<\/p>\n\n\r\n              \n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/multiplicaci&oacute;n-de-n&uacute;meros-complejos-1.gif\" alt=\"Explicaciones y ejemplos de multiplicaci&oacute;n de n&uacute;meros complejos - 1\"  ><\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\">6<sub>45\u00b0<\/sub> \u00b7 3<sub>15\u00b0 <\/sub> = <span class=\"esmeralda\">18<sub>60\u00b0<\/sub><\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><br \/><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Producto por  un complejo de m\u00f3dulo 1 <\/h2>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\"><strong>Al multiplicar un n\u00famero complejo z  = r<sub>\u03b1<\/sub> por 1<sub>\u03b2<\/sub> se gira z un \u00e1ngulo \u03b2 alrededor del origen.<\/strong><\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\"><span class=\"sol\">r<sub>\u03b1<\/sub> \u00b7 1<sub>\u03b2<\/sub> =  r<sub>\u03b1 + \u03b2<\/sub><\/span><\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/multiplicaci&oacute;n-de-n&uacute;meros-complejos-2.gif\" alt=\"Explicaciones y ejemplos de multiplicaci&oacute;n de n&uacute;meros complejos - 2\"  ><\/p>\n\n\n<\/section>","protected":false},"excerpt":{"rendered":"<p>Multiplicaci\u00f3n de n\u00fameros complejos en forma bin\u00f3mica El producto de los n\u00fameros complejos se realiza aplicando la propiedad distributiva del producto respecto de la suma y teniendo en cuenta que i2 = \u22121. (a + bi) \u00b7 (c + di) = (ac \u2212 bd) + (ad + bc)i ( 5 + 2 i) \u00b7 ( [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_seopress_robots_primary_cat":"","_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","advgb_blocks_editor_width":"","advgb_blocks_columns_visual_guide":"","footnotes":""},"categories":[377],"tags":[373],"class_list":["post-114792","post","type-post","status-publish","format-standard","hentry","category-aritmetica","tag-m"],"acf":[],"author_meta":{"display_name":"Andra","author_link":"https:\/\/www.superprof.es\/diccionario\/author\/andra"},"featured_img":null,"coauthors":[],"tax_additional":{"categories":{"linked":["<a href=\"https:\/\/www.superprof.es\/diccionario\/matematicas\/aritmetica\" class=\"advgb-post-tax-term\">Aritm\u00e9tica<\/a>"],"unlinked":["<span class=\"advgb-post-tax-term\">Aritm\u00e9tica<\/span>"]},"tags":{"linked":["<a href=\"https:\/\/www.superprof.es\/diccionario\/matematicas\/aritmetica\" class=\"advgb-post-tax-term\">m<\/a>"],"unlinked":["<span class=\"advgb-post-tax-term\">m<\/span>"]}},"comment_count":"0","relative_dates":{"created":"Publicado 7 a\u00f1os hace","modified":"Actualizado 2 semanas hace"},"absolute_dates":{"created":"Publicado el 29 enero 2020","modified":"Actualizado el 7 octubre 2026"},"absolute_dates_time":{"created":"Publicado el 29 enero 2020 18 h 19 min","modified":"Actualizado el 7 octubre 2026 17 h 43 min"},"featured_img_caption":"","series_order":"","_links":{"self":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/114792","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/comments?post=114792"}],"version-history":[{"count":4,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/114792\/revisions"}],"predecessor-version":[{"id":141331,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/114792\/revisions\/141331"}],"wp:attachment":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/media?parent=114792"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/categories?post=114792"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/tags?post=114792"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}