document.write( "Question 1073485: z-|z|=8+4i
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Algebra.Com's Answer #688314 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "let z = x + yi, where x and y are real\r\n" );
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document.write( "Substitute in\r\n" );
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document.write( "\"z+-+abs%28z%29+\"\"%22%22=%22%22\"\"+8+%2B+4i\"\r\n" );
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document.write( "\"x+%2B+yi+-+abs%28x+%2B+iy%29+\"\"%22%22=%22%22\"\"+8+%2B+4i%0D%0A%0D%0A%7B%7B%7Bx+%2B+yi+-+sqrt%28x%5E2+%2B+y%5E2%29+\"\"%22%22=%22%22\"\"+8+%2B+4i\"\r\n" );
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document.write( "Set real parts equal, and imaginary parts equal:\r\n" );
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document.write( "\"x-sqrt%28x%5E2%2By%5E2%29\"\"%22%22=%22%22\"\"8\",  \"yi+\"\"%22%22=%22%22\"\"+4i\"\r\n" );
document.write( "                   \"y+\"\"%22%22=%22%22\"\"+4\"\r\n" );
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document.write( "Substitute y=4\r\n" );
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document.write( "\"x-sqrt%28x%5E2%2B4%5E2%29\"\"%22%22=%22%22\"\"8\"\r\n" );
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document.write( "\"x-sqrt%28x%5E2%2B16%29\"\"%22%22=%22%22\"\"8\"\r\n" );
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document.write( "\"x-8\"\"%22%22=%22%22\"\"sqrt%28x%5E2%2B16%29\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"x%5E2-16x%2B64\"\"%22%22=%22%22\"\"x%5E2%2B16\"\r\n" );
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document.write( "Cancel the x2's\r\n" );
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document.write( "\"-16x%2B64\"\"%22%22=%22%22\"\"16\"\r\n" );
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document.write( "\"-16x\"\"%22%22=%22%22\"\"-48\"\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"3\"\r\n" );
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document.write( "But we must check to see if 3 is \r\n" );
document.write( "a solution or only an extraneous answer.\r\n" );
document.write( "Substitute in:\r\n" );
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document.write( "\"x-sqrt%28x%5E2%2B16%29\"\"%22%22=%22%22\"\"8\"\r\n" );
document.write( "\"3-sqrt%283%5E2%2B16%29\"\"%22%22=%22%22\"\"8\"\r\n" );
document.write( "\"3-sqrt%289%2B16%29\"\"%22%22=%22%22\"\"8\"\r\n" );
document.write( "\"3-sqrt%2825%29\"\"%22%22=%22%22\"\"8\"\r\n" );
document.write( "\"3-5\"\"%22%22=%22%22\"\"8\"\r\n" );
document.write( "\"-2\"\"%22%22=%22%22\"\"8\"\r\n" );
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document.write( "That's false so 3 is extraneous and there\r\n" );
document.write( "is no solution.\r\n" );
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document.write( "Edwin
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