Funciones Senoidales y N\u00fameros Complejos<\/title>\n <style>\n body {\n font-family: Arial, sans-serif;\n line-height: 1.6;\n margin: 20px;\n }\n h2 {\n color: #0056b3;\n }\n code {\n background-color: #f0f0f0;\n padding: 5px;\n display: block;\n margin: 10px 0;\n }\n <\/style>\n<\/head>\n<body>\n <h2>1. Funciones Senoidales<\/h2>\n <p>Las <strong>funciones senoidales<\/strong> son funciones matem\u00e1ticas que representan movimientos u oscilaciones peri\u00f3dicas, como las que se encuentran en la corriente alterna (CA) y en las ondas de sonido. La forma general de una funci\u00f3n senoidal es:<\/p>\n <code>y(t) = A · sin(ω t + φ)<\/code>\n <p>Donde:<\/p>\n <ul>\n <li><strong>A<\/strong>: Amplitud, el valor m\u00e1ximo de la onda.<\/li>\n <li><strong>ω<\/strong>: Frecuencia angular, dada en radianes por segundo.<\/li>\n <li><strong>t<\/strong>: Tiempo.<\/li>\n <li><strong>φ<\/strong>: Desfase, que indica un desplazamiento horizontal de la onda respecto al origen.<\/li>\n <\/ul>\n\n\n\n\n\n\n\n<h4 class=\"wp-block-heading\"> Los Fasores pueden representarse de 3 formas<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"498\" height=\"164\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image.png\" alt=\"\" class=\"wp-image-3575\" style=\"width:358px;height:auto\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image.png 498w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-300x99.png 300w\" sizes=\"auto, (max-width: 498px) 100vw, 498px\" \/><\/figure><\/div>\n\n\n<h2>2. Equivalencia con N\u00fameros Complejos<\/h2>\n <p>Las funciones senoidales tienen una relaci\u00f3n directa con los n\u00fameros complejos a trav\u00e9s de la <strong>f\u00f3rmula de Euler<\/strong>, que establece que una funci\u00f3n exponencial compleja puede representar tanto el seno como el coseno:<\/p>\n <code>e<sup>jθ<\/sup> = cos(θ) + j sin(θ)<\/code>\n <p>Por lo tanto, una se\u00f1al senoidal puede expresarse en t\u00e9rminos de n\u00fameros complejos como:<\/p>\n <code>A · e<sup>j(ω t + φ)<\/sup> = A [cos(ω t + φ) + j sin(ω t + φ)]<\/code>\n\n <h2>3. Conversiones de Coordenadas<\/h2>\n\n <h3>a. De Polar a Rectangular<\/h3>\n <p>En la forma polar, un n\u00famero complejo se expresa como:<\/p>\n <code>z = r ∠ θ<\/code>\n <p>Donde:<\/p>\n <ul>\n <li><strong>r<\/strong>: Magnitud del n\u00famero complejo.<\/li>\n <li><strong>θ<\/strong>: \u00c1ngulo de fase (en radianes o grados).<\/li>\n <\/ul>\n <p>Para convertir de polar a rectangular, usamos la f\u00f3rmula:<\/p>\n <code>z = r · [cos(θ) + j sin(θ)]<\/code>\n <p>Las componentes <strong>x<\/strong> (parte real) e <strong>y<\/strong> (parte imaginaria) del n\u00famero complejo en forma rectangular son:<\/p>\n <code>x = r · cos(θ)<\/code><br>\n <code>y = r · sin(θ)<\/code>\n\n <h3>b. De Rectangular a Polar<\/h3>\n <p>Para convertir un n\u00famero complejo de la forma rectangular <code>z = x + jy<\/code> a su equivalente polar:<\/p>\n <p>La magnitud se calcula como:<\/p>\n \n \n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"118\" height=\"45\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-3.png\" alt=\"\" class=\"wp-image-3594\"\/><\/figure><\/div>\n\n\n<p>El \u00e1ngulo se determina como:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"127\" height=\"49\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-4.png\" alt=\"\" class=\"wp-image-3598\"\/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading has-vivid-green-cyan-color has-text-color has-link-color wp-elements-c45c8ea514d2dc883d55f90dabfd4c1a\">4. Ejemplos Gr\u00e1ficos<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-465411f21023bdc16f301ff038af2351\">Ejemplo 1: Conversi\u00f3n de Polar a Rectangular<\/h3>\n\n\n\n \n <p>Dado <code>z = 5 ∠ 53°<\/code><\/p>\n <p>Convertimos a coordenadas rectangulares:<\/p>\n <code>x = 5 · cos(53°) ≈ 5 · 0.6018 = 3.01<\/code><br>\n <code>y = 5 · sin(53°) ≈ 5 · 0.7986 = 3.99<\/code>\n <p>Entonces, en forma rectangular:<\/p>\n <code>z ≈ 3.01 + j3.99<\/code>\n\n\n\n<h3 class=\"wp-block-heading has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-0ee2e13a60f5d74a1900c846efc23c8a\">Ejemplo 2: Conversi\u00f3n de Polar a Rectangular<\/h3>\n\n\n\n<p>Funci\u00f3n senoidal:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"224\" height=\"35\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-5.png\" alt=\"\" class=\"wp-image-3601\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li> <strong>Magnitud (A)<\/strong>: 10<\/li>\n\n\n\n<li><strong>\u00c1ngulo de fase (\u03b8)<\/strong>: 45\u00b0<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-7ef5aafc1a9211d286f212f6eb4f6a36\">Conversi\u00f3n a Fasor: El fasor correspondiente es:<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"102\" height=\"20\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-6.png\" alt=\"\" class=\"wp-image-3602\"\/><\/figure><\/div>\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"581\" height=\"393\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-7.png\" alt=\"\" class=\"wp-image-3603\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-7.png 581w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-7-300x203.png 300w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-7-75x50.png 75w\" sizes=\"auto, (max-width: 581px) 100vw, 581px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-6d63d1d7261de9978af3df5925342f36\">Ejemplo 1: Conversi\u00f3n de Rectangular a Polar<\/h3>\n\n\n\n \n <p>Dado <code>z = 3 + j4<\/code><\/p>\n <p>La magnitud es:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"309\" height=\"39\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-1.png\" alt=\"\" class=\"wp-image-3591\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-1.png 309w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-1-300x38.png 300w\" sizes=\"auto, (max-width: 309px) 100vw, 309px\" \/><\/figure><\/div>\n\n\n<p>El \u00e1ngulo es:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"182\" height=\"59\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-2.png\" alt=\"\" class=\"wp-image-3592\"\/><\/figure><\/div>\n\n\n <p>Entonces, en forma polar:<\/p>\n <code>z = 5 ∠ 53°<\/code>\n<\/body>\n<\/html>\u00e1ngulo es:<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-5d5808ea82b0c70d42668ecd37ce31de\">Ejemplo 2: Conversi\u00f3n de Rectangular a Polar<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"566\" height=\"426\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-8.png\" alt=\"\" class=\"wp-image-3604\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-8.png 566w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-8-300x226.png 300w\" sizes=\"auto, (max-width: 566px) 100vw, 566px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-260bb7061569108daa2239fe762542e8\">Operaciones Aritm\u00e9ticas con N\u00fameros Complejos<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"520\" height=\"191\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-11.png\" alt=\"\" class=\"wp-image-3608\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-11.png 520w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-11-300x110.png 300w\" sizes=\"auto, (max-width: 520px) 100vw, 520px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"605\" height=\"190\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-10.png\" alt=\"\" class=\"wp-image-3606\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-10.png 605w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-10-300x94.png 300w\" sizes=\"auto, (max-width: 605px) 100vw, 605px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading has-white-color has-black-background-color has-text-color has-background has-link-color wp-elements-019010d4ffaa0e6ba314b4964db12d90\"> Ejercicio 1: <strong>Conversi\u00f3n de Funci\u00f3n Senoidal a Fasor y de Polar a Rectangular<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"459\" height=\"147\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-14.png\" alt=\"\" class=\"wp-image-3612\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-14.png 459w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-14-300x96.png 300w\" sizes=\"auto, (max-width: 459px) 100vw, 459px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading has-white-color has-black-background-color has-text-color has-background has-link-color wp-elements-7c7164ebe7f4eb1100ce8e18da5ff97a\"> Ejercicio 2: <strong>Operaciones con N\u00fameros Complejos en Forma Polar y Rectangular<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"590\" height=\"230\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-15.png\" alt=\"\" class=\"wp-image-3613\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-15.png 590w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-15-300x117.png 300w\" sizes=\"auto, (max-width: 590px) 100vw, 590px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>\ufffc Funciones Senoidales y N\u00fameros Complejos 1. Funciones Senoidales Las funciones senoidales son funciones matem\u00e1ticas que representan movimientos u oscilaciones peri\u00f3dicas, como las que se encuentran en la corriente alterna (CA) y en las ondas de sonido. La forma general de una funci\u00f3n senoidal es: y(t) = A · sin(ω t + φ) Donde: A: … <a href=\"https:\/\/lash.utrng.edu.mx\/?p=3566\">Seguir leyendo <span class=\"meta-nav\">→<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[89],"tags":[],"class_list":["post-3566","post","type-post","status-publish","format-standard","hentry","category-primpar-electind"],"_links":{"self":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/3566","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3566"}],"version-history":[{"count":11,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/3566\/revisions"}],"predecessor-version":[{"id":3614,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/3566\/revisions\/3614"}],"wp:attachment":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3566"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3566"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3566"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

{"id":3566,"date":"2024-09-08T22:15:23","date_gmt":"2024-09-08T22:15:23","guid":{"rendered":"https:\/\/lash.utrng.edu.mx\/?p=3566"},"modified":"2024-09-18T02:23:20","modified_gmt":"2024-09-18T02:23:20","slug":"fasores","status":"publish","type":"post","link":"https:\/\/lash.utrng.edu.mx\/?p=3566","title":{"rendered":"Fasores"},"content":{"rendered":"\n\ufffc\n\n\n \n \n Funciones Senoidales y N\u00fameros Complejos<\/title>\n <style>\n body {\n font-family: Arial, sans-serif;\n line-height: 1.6;\n margin: 20px;\n }\n h2 {\n color: #0056b3;\n }\n code {\n background-color: #f0f0f0;\n padding: 5px;\n display: block;\n margin: 10px 0;\n }\n <\/style>\n<\/head>\n<body>\n <h2>1. Funciones Senoidales<\/h2>\n <p>Las <strong>funciones senoidales<\/strong> son funciones matem\u00e1ticas que representan movimientos u oscilaciones peri\u00f3dicas, como las que se encuentran en la corriente alterna (CA) y en las ondas de sonido. La forma general de una funci\u00f3n senoidal es:<\/p>\n <code>y(t) = A · sin(ω t + φ)<\/code>\n <p>Donde:<\/p>\n <ul>\n <li><strong>A<\/strong>: Amplitud, el valor m\u00e1ximo de la onda.<\/li>\n <li><strong>ω<\/strong>: Frecuencia angular, dada en radianes por segundo.<\/li>\n <li><strong>t<\/strong>: Tiempo.<\/li>\n <li><strong>φ<\/strong>: Desfase, que indica un desplazamiento horizontal de la onda respecto al origen.<\/li>\n <\/ul>\n\n\n\n\n\n\n\n<h4 class=\"wp-block-heading\"> Los Fasores pueden representarse de 3 formas<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"498\" height=\"164\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image.png\" alt=\"\" class=\"wp-image-3575\" style=\"width:358px;height:auto\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image.png 498w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-300x99.png 300w\" sizes=\"auto, (max-width: 498px) 100vw, 498px\" \/><\/figure><\/div>\n\n\n<h2>2. Equivalencia con N\u00fameros Complejos<\/h2>\n <p>Las funciones senoidales tienen una relaci\u00f3n directa con los n\u00fameros complejos a trav\u00e9s de la <strong>f\u00f3rmula de Euler<\/strong>, que establece que una funci\u00f3n exponencial compleja puede representar tanto el seno como el coseno:<\/p>\n <code>e<sup>jθ<\/sup> = cos(θ) + j sin(θ)<\/code>\n <p>Por lo tanto, una se\u00f1al senoidal puede expresarse en t\u00e9rminos de n\u00fameros complejos como:<\/p>\n <code>A · e<sup>j(ω t + φ)<\/sup> = A [cos(ω t + φ) + j sin(ω t + φ)]<\/code>\n\n <h2>3. Conversiones de Coordenadas<\/h2>\n\n <h3>a. De Polar a Rectangular<\/h3>\n <p>En la forma polar, un n\u00famero complejo se expresa como:<\/p>\n <code>z = r ∠ θ<\/code>\n <p>Donde:<\/p>\n <ul>\n <li><strong>r<\/strong>: Magnitud del n\u00famero complejo.<\/li>\n <li><strong>θ<\/strong>: \u00c1ngulo de fase (en radianes o grados).<\/li>\n <\/ul>\n <p>Para convertir de polar a rectangular, usamos la f\u00f3rmula:<\/p>\n <code>z = r · [cos(θ) + j sin(θ)]<\/code>\n <p>Las componentes <strong>x<\/strong> (parte real) e <strong>y<\/strong> (parte imaginaria) del n\u00famero complejo en forma rectangular son:<\/p>\n <code>x = r · cos(θ)<\/code><br>\n <code>y = r · sin(θ)<\/code>\n\n <h3>b. De Rectangular a Polar<\/h3>\n <p>Para convertir un n\u00famero complejo de la forma rectangular <code>z = x + jy<\/code> a su equivalente polar:<\/p>\n <p>La magnitud se calcula como:<\/p>\n \n \n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"118\" height=\"45\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-3.png\" alt=\"\" class=\"wp-image-3594\"\/><\/figure><\/div>\n\n\n<p>El \u00e1ngulo se determina como:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"127\" height=\"49\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-4.png\" alt=\"\" class=\"wp-image-3598\"\/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading has-vivid-green-cyan-color has-text-color has-link-color wp-elements-c45c8ea514d2dc883d55f90dabfd4c1a\">4. Ejemplos Gr\u00e1ficos<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-465411f21023bdc16f301ff038af2351\">Ejemplo 1: Conversi\u00f3n de Polar a Rectangular<\/h3>\n\n\n\n \n <p>Dado <code>z = 5 ∠ 53°<\/code><\/p>\n <p>Convertimos a coordenadas rectangulares:<\/p>\n <code>x = 5 · cos(53°) ≈ 5 · 0.6018 = 3.01<\/code><br>\n <code>y = 5 · sin(53°) ≈ 5 · 0.7986 = 3.99<\/code>\n <p>Entonces, en forma rectangular:<\/p>\n <code>z ≈ 3.01 + j3.99<\/code>\n\n\n\n<h3 class=\"wp-block-heading has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-0ee2e13a60f5d74a1900c846efc23c8a\">Ejemplo 2: Conversi\u00f3n de Polar a Rectangular<\/h3>\n\n\n\n<p>Funci\u00f3n senoidal:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"224\" height=\"35\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-5.png\" alt=\"\" class=\"wp-image-3601\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li> <strong>Magnitud (A)<\/strong>: 10<\/li>\n\n\n\n<li><strong>\u00c1ngulo de fase (\u03b8)<\/strong>: 45\u00b0<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-7ef5aafc1a9211d286f212f6eb4f6a36\">Conversi\u00f3n a Fasor: El fasor correspondiente es:<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"102\" height=\"20\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-6.png\" alt=\"\" class=\"wp-image-3602\"\/><\/figure><\/div>\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"581\" height=\"393\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-7.png\" alt=\"\" class=\"wp-image-3603\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-7.png 581w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-7-300x203.png 300w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-7-75x50.png 75w\" sizes=\"auto, (max-width: 581px) 100vw, 581px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-6d63d1d7261de9978af3df5925342f36\">Ejemplo 1: Conversi\u00f3n de Rectangular a Polar<\/h3>\n\n\n\n \n <p>Dado <code>z = 3 + j4<\/code><\/p>\n <p>La magnitud es:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"309\" height=\"39\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-1.png\" alt=\"\" class=\"wp-image-3591\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-1.png 309w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-1-300x38.png 300w\" sizes=\"auto, (max-width: 309px) 100vw, 309px\" \/><\/figure><\/div>\n\n\n<p>El \u00e1ngulo es:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"182\" height=\"59\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-2.png\" alt=\"\" class=\"wp-image-3592\"\/><\/figure><\/div>\n\n\n <p>Entonces, en forma polar:<\/p>\n <code>z = 5 ∠ 53°<\/code>\n<\/body>\n<\/html>\u00e1ngulo es:<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-5d5808ea82b0c70d42668ecd37ce31de\">Ejemplo 2: Conversi\u00f3n de Rectangular a Polar<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"566\" height=\"426\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-8.png\" alt=\"\" class=\"wp-image-3604\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-8.png 566w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-8-300x226.png 300w\" sizes=\"auto, (max-width: 566px) 100vw, 566px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-260bb7061569108daa2239fe762542e8\">Operaciones Aritm\u00e9ticas con N\u00fameros Complejos<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"520\" height=\"191\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-11.png\" alt=\"\" class=\"wp-image-3608\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-11.png 520w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-11-300x110.png 300w\" sizes=\"auto, (max-width: 520px) 100vw, 520px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"605\" height=\"190\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-10.png\" alt=\"\" class=\"wp-image-3606\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-10.png 605w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-10-300x94.png 300w\" sizes=\"auto, (max-width: 605px) 100vw, 605px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading has-white-color has-black-background-color has-text-color has-background has-link-color wp-elements-019010d4ffaa0e6ba314b4964db12d90\"> Ejercicio 1: <strong>Conversi\u00f3n de Funci\u00f3n Senoidal a Fasor y de Polar a Rectangular<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"459\" height=\"147\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-14.png\" alt=\"\" class=\"wp-image-3612\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-14.png 459w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-14-300x96.png 300w\" sizes=\"auto, (max-width: 459px) 100vw, 459px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading has-white-color has-black-background-color has-text-color has-background has-link-color wp-elements-7c7164ebe7f4eb1100ce8e18da5ff97a\"> Ejercicio 2: <strong>Operaciones con N\u00fameros Complejos en Forma Polar y Rectangular<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"590\" height=\"230\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-15.png\" alt=\"\" class=\"wp-image-3613\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-15.png 590w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2024\/09\/image-15-300x117.png 300w\" sizes=\"auto, (max-width: 590px) 100vw, 590px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>\ufffc Funciones Senoidales y N\u00fameros Complejos 1. Funciones Senoidales Las funciones senoidales son funciones matem\u00e1ticas que representan movimientos u oscilaciones peri\u00f3dicas, como las que se encuentran en la corriente alterna (CA) y en las ondas de sonido. La forma general de una funci\u00f3n senoidal es: y(t) = A · sin(ω t + φ) Donde: A: … <a href=\"https:\/\/lash.utrng.edu.mx\/?p=3566\">Seguir leyendo <span class=\"meta-nav\">→<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[89],"tags":[],"class_list":["post-3566","post","type-post","status-publish","format-standard","hentry","category-primpar-electind"],"_links":{"self":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/3566","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3566"}],"version-history":[{"count":11,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/3566\/revisions"}],"predecessor-version":[{"id":3614,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/3566\/revisions\/3614"}],"wp:attachment":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3566"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3566"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3566"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}