{"id":8475,"date":"2016-12-16T03:25:26","date_gmt":"2016-12-16T03:25:26","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=8475"},"modified":"2017-05-11T12:02:05","modified_gmt":"2017-05-11T12:02:05","slug":"representing-complex-numbers-graphically","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/representing-complex-numbers-graphically\/","title":{"rendered":"Representing Complex Numbers Graphically (+ & -)"},"content":{"rendered":"

Representing Complex Numbers Graphically (+ &\u00a0-)<\/strong><\/span><\/h2>\n

Due to their unique nature, complex numbers<\/a> cannot be represented on a normal set of coordinate axes.<\/p>\n

In 1806, J. R. Argand developed a method for displaying complex numbers<\/a> graphically as a point in a coordinate plane. His method, called the Argand diagram, establishes a relationship between the x-axis (real axis) with real numbers and the y-axis (imaginary axis) with imaginary numbers.<\/p>\n

In the Argand diagram, a complex number a + bi is the point (a,b) or the vector from the origin to the point (a,b).
\nGraph the complex numbers<\/strong>:<\/p>\n

1. 3 + 4i (3,4)<\/p>\n

2. 2 – 3i (2,-3)<\/p>\n

3. -4 + 2i (-4,2)<\/p>\n

4. 3 (which is really 3 + 0i) (3,0)<\/p>\n

5. 4i (which is really 0 + 4i) (0,4)<\/p>\n

The complex number<\/a> is represented by the point, or by the vector from the origin to the point.<\/p>\n

\"Representing-Complex-Numbers-Graphically-1\"<\/p>\n

Add 3 + 4i and -4 + 2i graphically.<\/p>\n

Graph the two complex numbers 3 + 4i and -4 + 2i as vectors.<\/p>\n

Create a parallelogram using these two vectors as adjacent sides.<\/p>\n

The answer to the addition is the vector forming the diagonal of the parallelogram (read from the origin).<\/p>\n

This new vector is called the resultant vector.<\/p>\n

\"Representing-Complex-Numbers-Graphically-2\"<\/p>\n

Subtract 3 + 4i from -2 + 2i<\/p>\n

Subtraction is the process of adding the additive inverse.
\n(-2 + 2i) – (3 + 4i)
\n= (-2 + 2i) + (-3 – 4i)
\n= (-5 – 2i)<\/p>\n

Graph the two complex numbers as vectors.<\/p>\n

Graph the additive inverse of the number being subtracted.<\/p>\n

Create a parallelogram using the first number and the additive inverse. The answer is the vector forming the diagonal of the parallelogram.<\/p>\n

\"Representing-Complex-Numbers-Graphically-3\"<\/p>\n","protected":false},"excerpt":{"rendered":"

Representing Complex Numbers Graphically (+ &\u00a0-) Due to their unique nature, complex numbers cannot be represented on a normal set of coordinate axes. In 1806, J. R. Argand developed a method for displaying complex numbers graphically as a point in a coordinate plane. His method, called the Argand diagram, establishes a relationship between the x-axis … Read more<\/a><\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[3077],"yoast_head":"\nRepresenting Complex Numbers Graphically (+ & -) - CBSE Library<\/title>\n<meta name=\"description\" content=\"Representing Complex Numbers\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/cbselibrary.com\/representing-complex-numbers-graphically\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Representing Complex Numbers Graphically (+ & -)\" \/>\n<meta property=\"og:description\" content=\"Representing Complex Numbers\" \/>\n<meta property=\"og:url\" content=\"https:\/\/cbselibrary.com\/representing-complex-numbers-graphically\/\" \/>\n<meta property=\"og:site_name\" content=\"CBSE Library\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/aplustopper\/\" \/>\n<meta property=\"article:published_time\" content=\"2016-12-16T03:25:26+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2017-05-11T12:02:05+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/c3.staticflickr.com\/6\/5598\/30831405434_0c0e11b000_o.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Raju\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Organization\",\"@id\":\"https:\/\/cbselibrary.com\/#organization\",\"name\":\"Aplus Topper\",\"url\":\"https:\/\/cbselibrary.com\/\",\"sameAs\":[\"https:\/\/www.facebook.com\/aplustopper\/\"],\"logo\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/cbselibrary.com\/#logo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg\",\"contentUrl\":\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg\",\"width\":1585,\"height\":375,\"caption\":\"Aplus Topper\"},\"image\":{\"@id\":\"https:\/\/cbselibrary.com\/#logo\"}},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/cbselibrary.com\/#website\",\"url\":\"https:\/\/cbselibrary.com\/\",\"name\":\"CBSE Library\",\"description\":\"Improve your Grades\",\"publisher\":{\"@id\":\"https:\/\/cbselibrary.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/cbselibrary.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/cbselibrary.com\/representing-complex-numbers-graphically\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/c3.staticflickr.com\/6\/5598\/30831405434_0c0e11b000_o.jpg\",\"contentUrl\":\"https:\/\/c3.staticflickr.com\/6\/5598\/30831405434_0c0e11b000_o.jpg\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/cbselibrary.com\/representing-complex-numbers-graphically\/#webpage\",\"url\":\"https:\/\/cbselibrary.com\/representing-complex-numbers-graphically\/\",\"name\":\"Representing Complex Numbers Graphically (+ & -) - 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