{"id":92,"date":"2023-09-21T19:43:47","date_gmt":"2023-09-21T19:43:47","guid":{"rendered":"https:\/\/www.mirrorofimagination.com\/blog\/?p=92"},"modified":"2023-09-23T04:27:39","modified_gmt":"2023-09-23T04:27:39","slug":"numeric-approximations-to-the-imaginary-number-the-imaginary-value","status":"publish","type":"post","link":"https:\/\/www.mirrorofimagination.com\/blog\/numeric-approximations-to-the-imaginary-number-the-imaginary-value\/","title":{"rendered":"Numeric approximations to the imaginary number: the imaginary value"},"content":{"rendered":"\n<p><a href=\"https:\/\/www.mirrorofimagination.com\/blog\/numeric-approximations-to-the-imaginary-number-representations-of-negative-numbers\/\">Part 1<\/a><\/p>\n\n\n\n<p>With a number for -1, we can calculate the value of i. <\/p>\n\n\n\n<p>In base 2, &#8230;111 =-1, so we need a number x such that x^2 = &#8230;111. We can multiply by term order to iteratively solve.<\/p>\n\n\n\n<p>For the first term:<\/p>\n\n\n\n<p>1 = x0*x0<\/p>\n\n\n\n<p>So x0=1<\/p>\n\n\n\n<p>Second term:<\/p>\n\n\n\n<p>1 = x1*1 + 1*x1<\/p>\n\n\n\n<p>1 = 2*x1<\/p>\n\n\n\n<p>So x1 = 1\/2<\/p>\n\n\n\n<p>Third term:<\/p>\n\n\n\n<p>1 = x2*1 + (1\/2)*(1\/2) + 1*x2<\/p>\n\n\n\n<p>1 = 2*X2 + 1\/4<\/p>\n\n\n\n<p>3\/4 = 2*X2<\/p>\n\n\n\n<p>So x2 = 3\/8<\/p>\n\n\n\n<p>And so on. We now have a numeric representation of i in base 2.<\/p>\n\n\n\n<p>&#8230; (35\/128) (5\/16) (3\/8) (1\/2) (1)<\/p>\n\n\n\n<p>Next time we will investigate some properties of this number.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Part 1 With a number for -1, we can calculate the value of i. In base 2, &#8230;111 =-1, so we need a number x such that x^2 = &#8230;111. We can multiply by term order to iteratively solve. For the first term: 1 = x0*x0 So x0=1 Second term: 1 = x1*1 + 1*x1&hellip; <a class=\"more-link\" href=\"https:\/\/www.mirrorofimagination.com\/blog\/numeric-approximations-to-the-imaginary-number-the-imaginary-value\/\">Continue reading <span class=\"screen-reader-text\">Numeric approximations to the imaginary number: the imaginary value<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,5],"tags":[],"class_list":["post-92","post","type-post","status-publish","format-standard","hentry","category-imaginary-number","category-nonfiction","entry"],"_links":{"self":[{"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/posts\/92","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/comments?post=92"}],"version-history":[{"count":2,"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/posts\/92\/revisions"}],"predecessor-version":[{"id":104,"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/posts\/92\/revisions\/104"}],"wp:attachment":[{"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/media?parent=92"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/categories?post=92"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mirrorofimagination.com\/blog\/wp-json\/wp\/v2\/tags?post=92"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}