{"id":3099,"date":"2014-04-13T04:13:43","date_gmt":"2014-04-13T02:13:43","guid":{"rendered":"http:\/\/www.ilkkimbuldu.com\/?p=3099"},"modified":"2018-02-28T01:32:07","modified_gmt":"2018-02-27T23:32:07","slug":"karmasik-sayilari-kim-buldu","status":"publish","type":"post","link":"https:\/\/www.ilkkimbuldu.com\/?p=3099","title":{"rendered":"Karma\u015f\u0131k Say\u0131lar\u0131 kim buldu"},"content":{"rendered":"<p>Karma\u015f\u0131k say\u0131lar a ve b ger\u00e7el\u00a0say\u0131 ve i, -l\u2019in karek\u00f6k\u00fc olmak \u00fczere a+ib \u015feklinde yaz\u0131labilen say\u0131lar. Burada a, karma\u015f\u0131k say\u0131n\u0131n\u00a0ger\u00e7el k\u0131sm\u0131n\u0131 ve b sanal k\u0131sm\u0131n\u0131 te\u015fkil eder.<\/p>\n<p>T\u00e2rihi\u00a0Negatif say\u0131lar\u0131n bulunmas\u0131ndan sonra, matematik\u00e7iler karesi negatif say\u0131 olan say\u0131y\u0131 arad\u0131lar. ilk\u00a0matematik\u00e7iler b\u00f6yle bir say\u0131n\u0131n mevcut olmad\u0131\u011f\u0131 sonucuna vard\u0131lar. 1637\u2019de <strong>Ren\u00e9 Descartes<\/strong> bu t\u00fcr\u00a0say\u0131lar\u0131n varl\u0131\u011f\u0131na dikkati \u00e7ekmi\u015ftir.<\/p>\n<p>1777\u2019de <a href=\"http:\/\/www.ilkkimbuldu.com\/leonhard-euler-kimdir\/\">Leonhard Euler<\/a> g\u00fcn\u00fcm\u00fczdeki i say\u0131s\u0131n\u0131 sembol olarak\u00a0kullanm\u0131\u015ft\u0131r. Karma\u015f\u0131k s\u00f6z\u00fc ilk def\u00e2 Gauss taraf\u0131ndan verilmi\u015ftir. Elektrik ve ma\u011fnetizman\u0131n\u00a0matematiksel if\u00e2desinde karma\u015f\u0131k say\u0131lar \u00e7ok \u00f6nemli rol oynamaktad\u0131r.<\/p>\n<p>Matematikte <b>karma\u015f\u0131k say\u0131<\/b>, bir ger\u00e7el bir de sanal k\u0131s\u0131mdan olu\u015fan bir nesnedir. a ve b say\u0131lar\u0131 ger\u00e7ek olursa karma\u015f\u0131k say\u0131lar \u015fu bi\u00e7imde g\u00f6sterilirler:<\/p>\n<dl>\n<dd><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/7af906be1b59d40e140f50d0c28edb1b344ed951\" alt=\"{\\displaystyle z=a+\\mathbf {i} b\\,}\" \/><\/dd>\n<\/dl>\n<p>Genel olarak karma\u015f\u0131k say\u0131lar i\u00e7in &#8220;z&#8221; harfi kullan\u0131l\u0131r. <img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/7727c9b6cb4a3d52bb9172453acba7047ddcbb56\" alt=\"{\\displaystyle \\mathbf {i} ^{2}=-1}\" \/> \u00f6zelli\u011fini sa\u011flayan sanal birime <img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/dc909dd0c91a68cdb9cda4ae133fa1f82c987c01\" alt=\"{\\displaystyle \\mathbf {i} }\" \/> denir. Kimi zaman \u00f6zellikle elektrik m\u00fchendisli\u011finde <img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/dc909dd0c91a68cdb9cda4ae133fa1f82c987c01\" alt=\"{\\displaystyle \\mathbf {i} }\" \/> yerine, <img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/ca5d874dbb32b8b33e83ca521f592808387a486e\" alt=\"{\\displaystyle \\mathbf {j} }\" \/> kullan\u0131l\u0131r.<\/p>\n<p>Ayr\u0131ca matematikte bu say\u0131lar\u0131n uzay\u0131 <span class=\"mwe-math-mathml-inline mwe-math-mathml-a11y\">{\\displaystyle \\mathbb {C} }<\/span><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f9add4085095b9b6d28d045fd9c92c2c09f549a7\" alt=\"{\\displaystyle \\mathbb {C} }\" \/> olarak g\u00f6sterilir. Bu harfin se\u00e7ilmesinin nedeni \u0130ngilizce&#8217;de <i>karma\u015f\u0131k<\/i> s\u00f6zc\u00fc\u011f\u00fcn\u00fcn kar\u015f\u0131l\u0131\u011f\u0131 olarak <i>complex<\/i> s\u00f6zc\u00fc\u011f\u00fcn\u00fcn kullan\u0131lmas\u0131d\u0131r, nitekim baz\u0131 T\u00fcrk\u00e7e kaynaklarda <i>complex<\/i> s\u00f6zc\u00fc\u011f\u00fcnden dev\u015firilen <i>kompleks<\/i> s\u00f6zc\u00fc\u011f\u00fcne de raslanabilir. Karma\u015f\u0131k say\u0131lara b\u00f6yle bir ad\u0131n verilmesinin nedeni ise a\u015fa\u011f\u0131da da g\u00f6rece\u011fimiz gibi ger\u00e7el ve sanal k\u0131s\u0131mlar\u0131n bir arada durmas\u0131d\u0131r.<\/p>\n<p>B\u00fct\u00fcn ger\u00e7el say\u0131lar sanal k\u0131s\u0131mlar\u0131 s\u0131f\u0131ra e\u015fit olan birer karma\u015f\u0131k say\u0131 olarak d\u00fc\u015f\u00fcn\u00fclebilir. Di\u011fer bir deyi\u015fle ger\u00e7el say\u0131lar, karma\u015f\u0131k say\u0131 d\u00fczleminde ger\u00e7el say\u0131lar ekseni \u00fczerinde bulunurlar.<\/p>\n<dl>\n<dd><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/b84651accd5a69f3a02ae5289ca1ac98c97478a0\" alt=\"{\\displaystyle z=a+\\mathbf {i} \\cdot 0\\in \\mathbb {R} }\" \/><\/dd>\n<\/dl>\n<p>Bir z karma\u015f\u0131k say\u0131s\u0131n\u0131n ger\u00e7el ve sanal par\u00e7alar\u0131 s\u0131ras\u0131yla Re(z) ve Im(z) fonksiyonlar\u0131yla g\u00f6sterilir. B\u00fct\u00fcn bu tan\u0131mlar\u0131 ve \u00f6zellikleri bir \u00f6rnekte g\u00f6sterelim. <img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/a58a4f609a1bd90d064ee22c4fb2a322a1cdd4ff\" alt=\"{\\displaystyle z=4-7\\mathbf {i} }\" \/> say\u0131s\u0131 ger\u00e7el k\u0131sm\u0131 Re(4-7<b>i<\/b>)=4, sanal k\u0131sm\u0131 Im(4-7<b>i<\/b>)=-7 olan <img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f9add4085095b9b6d28d045fd9c92c2c09f549a7\" alt=\"{\\displaystyle \\mathbb {C} }\" \/> uzay\u0131nda bir karma\u015f\u0131k say\u0131d\u0131r.Bunun d\u0131\u015f\u0131nda karma\u015f\u0131k say\u0131lar\u0131n ba\u015fka \u00f6zellikleri de vard\u0131r. \u00d6rne\u011fin bir karma\u015f\u0131k say\u0131 d\u00fczlemde bir vekt\u00f6r olarak temsil edilebilir.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Karma\u015f\u0131k say\u0131lar a ve b ger\u00e7el\u00a0say\u0131 ve i, -l\u2019in karek\u00f6k\u00fc olmak \u00fczere a+ib \u015feklinde yaz\u0131labilen say\u0131lar. Burada a, karma\u015f\u0131k say\u0131n\u0131n\u00a0ger\u00e7el k\u0131sm\u0131n\u0131 ve b sanal k\u0131sm\u0131n\u0131 te\u015fkil eder. T\u00e2rihi\u00a0Negatif say\u0131lar\u0131n bulunmas\u0131ndan&#8230;<\/p>\n","protected":false},"author":1,"featured_media":10317,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[92],"tags":[2240,1210],"class_list":["post-3099","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-bilim","tag-karmasik-sayilar","tag-sayilar"],"_links":{"self":[{"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/posts\/3099"}],"collection":[{"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3099"}],"version-history":[{"count":5,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/posts\/3099\/revisions"}],"predecessor-version":[{"id":10318,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/posts\/3099\/revisions\/10318"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/media\/10317"}],"wp:attachment":[{"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3099"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3099"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3099"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}