document.write( "Question 1021503: Find all complex numbers z such that
\n" ); 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.
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Algebra.Com's Answer #637305 by robertb(5830)\"\" \"About 
You can put this solution on YOUR website!
Let z = x+iy
\n" ); document.write( "==> \r
\n" ); document.write( "\n" ); document.write( "= \"%28x%5E2%2By%5E2-2x-y%29%2Bi%28x%2B2y%29\"
\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 \"x%5E2%2By%5E2-2x-y+=+0\"\r
\n" ); document.write( "\n" ); document.write( "Putting x = 2-2y into \"x%5E2%2By%5E2-2x-y+=+0\", we get\r
\n" ); document.write( "\n" ); document.write( "\"4%281-y%29%5E2%2By%5E2-4%281-y%29+-+y+=+0\"\r
\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( "\"z%5B1%5D+=+2\", and \"z%5B2%5D+=+i\".
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