document.write( "Question 1172510: If z = $\"%28x%2Bi%28y%2B2%29%29%2F%28%28x%2B1%29%2Biy%29\"$ , w = x+iy and |z| = 2,\r
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\n" ); document.write( "\n" ); document.write( "The answer is \r
\n" ); document.write( "\n" ); document.write( " $\"%28x+%2B+4%2F3%29%5E2+%2B%28y-+2%2F3%29%5E2+=+20%2F9\"$ , but I'm having some complications with the working \n" ); document.write( "

Algebra.Com's Answer #797568 by ikleyn(52802) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "We are given that   = 2.\r\n" );
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document.write( "It implies  | x + i(y+2) | = 2 * |(x+1) + iy |.\r\n" );
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document.write( "In turn, it means that\r\n" );
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document.write( "    x^2 + (y+2)^2 = 4 * ((x+1)^2 + y^2).\r\n" );
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document.write( "Simplify it a bit\r\n" );
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document.write( "    x^2 + y^2 + 4y + 4 = 4*(x^2 + 2x + 1 + y^2),\r\n" );
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document.write( "    x^2 + 4y + y^2 + 4 = 4x^2 + 8x + 4 + 4y^2,\r\n" );
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document.write( "    3x^2 + 8x + 3y^2 - 4y = 0.\r\n" );
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document.write( "Complete the squares separately for x-terms and y-terms\r\n" );
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document.write( "    +  = \r\n" );
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document.write( "    +  = \r\n" );
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document.write( "    +  = .\r\n" );
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document.write( "It is EXACTLY the answer given in your post.\r\n" );
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document.write( "By the way, it is an equation of the circle of the radius of   =   centered at the point  (,).\r\n" );
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document.write( "So, the locus of  { w }  is the described circle.     ANSWER\r\n" );
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