{"id":809,"date":"2012-02-22T17:16:58","date_gmt":"2012-02-22T17:16:58","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=809"},"modified":"2014-12-02T08:33:48","modified_gmt":"2014-12-02T08:33:48","slug":"imaginary-unit","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/imaginary-unit\/","title":{"rendered":"Imaginary Numbers: Understanding the Imaginary Part"},"content":{"rendered":"<p>We are told that we cannot take square root of a negative number. However, we can take the square root of a negative number, but it involves using a new number to do it. This new number was called \u2018<em>i<\/em>\u2019 stands for imaginary. The imaginary is defined as:<\/p>\n<p><a href=\"https:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/2\/imaginary-unit.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-810\" src=\"https:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/2\/imaginary-unit.png\" alt=\"\" width=\"145\" height=\"206\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>The pattern of powers, sign, 1\u2019s and <em>i<\/em>\u2019s is cyclic:<\/p>\n<p><a href=\"https:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/2\/imaginary-unit-2.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-811\" src=\"https:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/2\/imaginary-unit-2.png\" alt=\"\" width=\"145\" height=\"210\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>To find high power of i, we can simplify the exponent by converting it to closest multiple of 4 plus the remainder, shown in the example below:<\/p>\n<p><a href=\"https:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/2\/imaginary-unit-3.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-812\" src=\"https:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/2\/imaginary-unit-3.png\" alt=\"\" width=\"176\" height=\"28\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Brockville visit: <a href=\"..\/..\/tutoring-in-brockville\/\">Tutoring in Brockville<\/a>.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We are told that we cannot take square root of a negative number. However, we can take the square root of a negative number, but it involves using a new number to do it. This new number was called \u2018i\u2019 stands for imaginary. The imaginary is defined as: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [&hellip;]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2,14],"tags":[914,1718],"class_list":["post-809","post","type-post","status-publish","format-standard","hentry","category-algebra","category-pre-calculus","tag-imaginaryunits","tag-squarerootofnegativenumbers"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/809","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=809"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/809\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=809"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=809"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=809"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}