document.write( "Question 1021503: Find all complex numbers z such that
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document.write( "|z|^2-2(con-z)+iz=2i, where the absolute value sign represents the distance of the complex number from the origin of a complex plane and (con-z) represents the complex conjugate of z. \n" );
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Algebra.Com's Answer #637305 by robertb(5830)![]() ![]() You can put this solution on YOUR website! Let z = x+iy \n" ); document.write( "==> \n" ); document.write( "\n" ); document.write( "= \n" ); document.write( "Since this is supposed to be equal to 2i, it follows that\r \n" ); document.write( "\n" ); document.write( "x+2y = 2 and \n" ); document.write( "\n" ); document.write( "Putting x = 2-2y into \n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Simplifying this and solving for y (you should be able to do the algebra!), we get\r \n" ); document.write( "\n" ); document.write( "y = 0 or y=1. \n" ); document.write( "The corresponding x-values are x = 2 or x = 0 respectively..\r \n" ); document.write( "\n" ); document.write( "Therefore there are two complex numbers satisfying the original equation namely\r \n" ); document.write( "\n" ); document.write( " |