{"id":460,"date":"2015-10-26T19:25:48","date_gmt":"2015-10-26T19:25:48","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&#038;p=460"},"modified":"2015-11-12T18:37:59","modified_gmt":"2015-11-12T18:37:59","slug":"key-concepts-glossary-13","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/chapter\/key-concepts-glossary-13\/","title":{"raw":"Key Concepts &amp; Glossary","rendered":"Key Concepts &amp; Glossary"},"content":{"raw":"<h2 data-type=\"title\">Key Concepts<\/h2>\r\n<ul id=\"fs-id1165135261454\">\r\n\t<li>The square root of any negative number can be written as a multiple of <em>i<\/em>.<\/li>\r\n\t<li>To plot a complex number, we use two number lines, crossed to form the complex plane. The horizontal axis is the real axis, and the vertical axis is the imaginary axis.<\/li>\r\n\t<li>Complex numbers can be added and subtracted by combining the real parts and combining the imaginary parts.<\/li>\r\n\t<li>Complex numbers can be multiplied and divided.<\/li>\r\n\t<li>To multiply complex numbers, distribute just as with polynomials.<\/li>\r\n\t<li>To divide complex numbers, multiply both the numerator and denominator by the complex conjugate of the denominator to eliminate the complex number from the denominator.<\/li>\r\n\t<li>The powers of <em>i<\/em>\u00a0are cyclic, repeating every fourth one.<\/li>\r\n<\/ul>\r\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\r\n<dl id=\"fs-id1165135320095\" class=\"definition\"><dt><strong>complex conjugate<\/strong><\/dt><dd id=\"fs-id1165135320101\">the complex number in which the sign of the imaginary part is changed and the real part of the number is left unchanged; when added to or multiplied by the original complex number, the result is a real number<\/dd><\/dl><dl id=\"fs-id1165135320107\" class=\"definition\"><dt><strong>complex number<\/strong><\/dt><dd id=\"fs-id1165135320112\">the sum of a real number and an imaginary number, written in the standard form <em>a<\/em> +\u00a0<em>bi<\/em>, where <em>a<\/em>\u00a0is the real part, and <em>bi<\/em>\u00a0is the imaginary part<\/dd><\/dl><dl id=\"fs-id1165133260439\" class=\"definition\"><dt><strong>complex plane<\/strong><\/dt><dd id=\"fs-id1165133260444\">a coordinate system in which the horizontal axis is used to represent the real part of a complex number and the vertical axis is used to represent the imaginary part of a complex number<\/dd><\/dl><dl id=\"fs-id1165133260450\" class=\"definition\"><dt><strong>imaginary number<\/strong><\/dt><dd id=\"fs-id1165133260456\">a number in the form <em>bi<\/em>\u00a0where [latex]i=\\sqrt{-1}\\\\[\/latex]<\/dd><\/dl>","rendered":"<h2 data-type=\"title\">Key Concepts<\/h2>\n<ul id=\"fs-id1165135261454\">\n<li>The square root of any negative number can be written as a multiple of <em>i<\/em>.<\/li>\n<li>To plot a complex number, we use two number lines, crossed to form the complex plane. The horizontal axis is the real axis, and the vertical axis is the imaginary axis.<\/li>\n<li>Complex numbers can be added and subtracted by combining the real parts and combining the imaginary parts.<\/li>\n<li>Complex numbers can be multiplied and divided.<\/li>\n<li>To multiply complex numbers, distribute just as with polynomials.<\/li>\n<li>To divide complex numbers, multiply both the numerator and denominator by the complex conjugate of the denominator to eliminate the complex number from the denominator.<\/li>\n<li>The powers of <em>i<\/em>\u00a0are cyclic, repeating every fourth one.<\/li>\n<\/ul>\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl id=\"fs-id1165135320095\" class=\"definition\">\n<dt><strong>complex conjugate<\/strong><\/dt>\n<dd id=\"fs-id1165135320101\">the complex number in which the sign of the imaginary part is changed and the real part of the number is left unchanged; when added to or multiplied by the original complex number, the result is a real number<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135320107\" class=\"definition\">\n<dt><strong>complex number<\/strong><\/dt>\n<dd id=\"fs-id1165135320112\">the sum of a real number and an imaginary number, written in the standard form <em>a<\/em> +\u00a0<em>bi<\/em>, where <em>a<\/em>\u00a0is the real part, and <em>bi<\/em>\u00a0is the imaginary part<\/dd>\n<\/dl>\n<dl id=\"fs-id1165133260439\" class=\"definition\">\n<dt><strong>complex plane<\/strong><\/dt>\n<dd id=\"fs-id1165133260444\">a coordinate system in which the horizontal axis is used to represent the real part of a complex number and the vertical axis is used to represent the imaginary part of a complex number<\/dd>\n<\/dl>\n<dl id=\"fs-id1165133260450\" class=\"definition\">\n<dt><strong>imaginary number<\/strong><\/dt>\n<dd id=\"fs-id1165133260456\">a number in the form <em>bi<\/em>\u00a0where [latex]i=\\sqrt{-1}\\\\[\/latex]<\/dd>\n<\/dl>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-460\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>College Algebra. <strong>Authored by<\/strong>: OpenStax College Algebra. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":276,"menu_order":6,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"College 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