{"id":52877,"date":"2026-07-23T16:30:12","date_gmt":"2026-07-23T16:30:12","guid":{"rendered":"https:\/\/www.oracletutoring.ca\/blog\/?p=52877"},"modified":"2026-07-23T16:30:13","modified_gmt":"2026-07-23T16:30:13","slug":"math-complex-numbers","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-complex-numbers\/","title":{"rendered":"Math: complex numbers"},"content":{"rendered":"\n<h2>Tutoring university level math, one might run into complex numbers. The tutor begins about them.<\/h2>\n<p>\nThe following is by my understanding.<\/p>\n<p>\nIn the Real number system, there is no square root of -1. Yet, in the Complex number system, sqrt(-1) = i. In some contexts, people call it j: sqrt(-1) = j. Therefore, depending on your context, i^2=-1 or j^2=-1. Herein, I will use i^2=-1.<\/p>\n<p>\nIt follows that, while the binomial x^2 + 1 doesn&#8217;t factor over the Real numbers, it does over the Complex numbers: x^2 + 1 = (x-i)(x+i), since -i^2 = 1.<\/p>\n<p>\nSince i^2=-1, (2i)^2=4(-1)=-4 and so on.<\/p>\n<p>\nI plan to continue about Complex numbers.<\/p>\n<p>\nSource:<\/p>\n<p>\nTravers, K.J., Dalton, L.C., Brunner, V.F., Taylor, A.R. (1977). <em>Using Advanced Algebra.<\/em> Doubleday Canada Limited.<\/p>\nJack of <a href=\"https:\/\/www.oracletutoring.ca\">Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.\n","protected":false},"excerpt":{"rendered":"<p>Tutoring university level math, one might run into complex numbers. The tutor begins about them. The &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/math-complex-numbers\/\"> <span class=\"screen-reader-text\">Math: complex numbers<\/span> Read more \u2192<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[4357,4358],"class_list":["post-52877","post","type-post","status-publish","format-standard","hentry","category-math","tag-complex-numbers","tag-square-roots-of-negative-numbers"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/52877","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=52877"}],"version-history":[{"count":3,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/52877\/revisions"}],"predecessor-version":[{"id":52880,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/52877\/revisions\/52880"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=52877"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=52877"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=52877"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}