Editing Complex number (section)

====Triangles====
Every triangle has a unique [[Steiner inellipse]] – an [[ellipse]] inside the triangle and tangent to the midpoints of the three sides of the triangle. The [[Focus (geometry)|foci]] of a triangle's Steiner inellipse can be found as follows, according to [[Marden's theorem]]:<ref>{{cite journal |last1=Kalman|first1=Dan|title=An Elementary Proof of Marden's Theorem |url=http://mathdl.maa.org/mathDL/22/?pa=content&sa=viewDocument&nodeId=3338&pf=1 |journal=[[American Mathematical Monthly]] |volume=115 |issue=4 |pages=330–38 |year=2008a |doi=10.1080/00029890.2008.11920532 |s2cid=13222698 |issn=0002-9890 |access-date=1 January 2012 |archive-url=https://web.archive.org/web/20120308104622/http://mathdl.maa.org/mathDL/22/?pa=content&sa=viewDocument&nodeId=3338&pf=1 |archive-date=8 March 2012|url-status=live}}</ref><ref>{{cite journal |last1=Kalman |first1=Dan |title=The Most Marvelous Theorem in Mathematics |url=http://mathdl.maa.org/mathDL/4/?pa=content&sa=viewDocument&nodeId=1663 |journal=[[Journal of Online Mathematics and Its Applications]] |year=2008b |access-date=1 January 2012|archive-url=https://web.archive.org/web/20120208014954/http://mathdl.maa.org/mathDL/4/?pa=content&sa=viewDocument&nodeId=1663 |archive-date=8 February 2012 |url-status=live}}</ref> Denote the triangle's vertices in the complex plane as {{math|1=''a'' = ''x''<sub>''A''</sub> + ''y''<sub>''A''</sub>''i''}}, {{math|1=''b'' = ''x''<sub>''B''</sub> + ''y''<sub>''B''</sub>''i''}}, and {{math|1=''c'' = ''x''<sub>''C''</sub> + ''y''<sub>''C''</sub>''i''}}. Write the [[cubic equation]] <math>(x-a)(x-b)(x-c)=0</math>, take its derivative, and equate the (quadratic) derivative to zero. Marden's theorem says that the solutions of this equation are the complex numbers denoting the locations of the two foci of the Steiner inellipse.