{"id":495,"date":"2016-10-27T01:09:07","date_gmt":"2016-10-27T06:09:07","guid":{"rendered":"http:\/\/thenoyes.com\/littlenoise\/?p=495"},"modified":"2016-10-27T11:48:00","modified_gmt":"2016-10-27T16:48:00","slug":"square-root-of-a-complex-number-using-compass-and-straight-edge-geometry","status":"publish","type":"post","link":"https:\/\/thenoyes.com\/littlenoise\/?p=495","title":{"rendered":"Square Root of a Complex Number using Compass and Straight Edge Geometry"},"content":{"rendered":"<p>Also available as an <a href=\"https:\/\/www.geogebra.org\/m\/nn3HcgVw\">interactive applet<\/a> (scrollwheel or pinch to zoom so you can adjust the axis how you want).<\/p>\n<p>Descartes allowed a line segment of unit length to find roots. The rest of the construction is completed with just Euclid&#8217;s compass and straight edge.<br \/>\n<a href=\"https:\/\/i0.wp.com\/thenoyes.com\/littlenoise\/wp-content\/uploads\/2016\/10\/Euclid-and-Descartes-complex-root.png?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/thenoyes.com\/littlenoise\/wp-content\/uploads\/2016\/10\/Euclid-and-Descartes-complex-root.png?resize=252%2C300&#038;ssl=1\" alt=\"euclid-and-descartes-complex-root\" width=\"252\" height=\"300\" class=\"alignnone size-medium wp-image-494\" srcset=\"https:\/\/i0.wp.com\/thenoyes.com\/littlenoise\/wp-content\/uploads\/2016\/10\/Euclid-and-Descartes-complex-root.png?resize=252%2C300&amp;ssl=1 252w, https:\/\/i0.wp.com\/thenoyes.com\/littlenoise\/wp-content\/uploads\/2016\/10\/Euclid-and-Descartes-complex-root.png?w=528&amp;ssl=1 528w\" sizes=\"auto, (max-width: 252px) 100vw, 252px\" \/><\/a><\/p>\n<p>Given: a complex number C plotted on the complex plane.<br \/>\nBisect the angle formed between C, the origin O, and the positive X (real) axis.<br \/>\nExtend OC past O by a unit line segment to U.<br \/>\nFind the midpoint, M, between U and C.<br \/>\nConstruct a half-circle centered at M through U and C.<br \/>\nDraw the perpendicular to UC through O to intersect the half-circle at I.<br \/>\nDraw a circle centered at O through I.<br \/>\nThe circle intersects the bisector at S.<br \/>\nS is a square root of C.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Also available as an interactive applet (scrollwheel or pinch to zoom so you can adjust the axis how you want). Descartes allowed a line segment of unit length to find roots. The rest of the construction is completed with just Euclid&#8217;s compass and straight edge. Given: a complex number C plotted on the complex plane. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[3],"tags":[],"class_list":["post-495","post","type-post","status-publish","format-standard","hentry","category-technical"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2IBF1-7Z","jetpack_sharing_enabled":true,"jetpack-related-posts":[],"_links":{"self":[{"href":"https:\/\/thenoyes.com\/littlenoise\/index.php?rest_route=\/wp\/v2\/posts\/495","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thenoyes.com\/littlenoise\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thenoyes.com\/littlenoise\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thenoyes.com\/littlenoise\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/thenoyes.com\/littlenoise\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=495"}],"version-history":[{"count":12,"href":"https:\/\/thenoyes.com\/littlenoise\/index.php?rest_route=\/wp\/v2\/posts\/495\/revisions"}],"predecessor-version":[{"id":507,"href":"https:\/\/thenoyes.com\/littlenoise\/index.php?rest_route=\/wp\/v2\/posts\/495\/revisions\/507"}],"wp:attachment":[{"href":"https:\/\/thenoyes.com\/littlenoise\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=495"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thenoyes.com\/littlenoise\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=495"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thenoyes.com\/littlenoise\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=495"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}