document.write( "Question 1157072: \"%28%281%2Bi%29%2F%281-i%29%29%5E2+%2B+1%2F%28x%2Biy%29+=+1%2Bi\" \n" ); document.write( "
Algebra.Com's Answer #779984 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"%28%281+%2B+i%29%2F%281+-+i%29%29%5E2+%2B+1%2F%28x+%2B+iy%29+=+1+%2B+i\" \r\n" );
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document.write( "We simplify what's squared in the the first term\r\n" );
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document.write( "Now we square it to get the complete first term simplified:\r\n" );
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document.write( "\"matrix%281%2C2%2Cfirst%2Cterm%29=%28%281+%2B+i%29%2F%281+-+i%29%29%5E2=i%5E2=-1\"\r\n" );
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document.write( "Substituting -1 for the first term\r\n" );
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document.write( "\"-1+%2B+1%2F%28x+%2B+iy%29+=+1+%2B+i\"\r\n" );
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document.write( "Add 1 to both sides:\r\n" );
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document.write( "\"1%2F%28x+%2B+iy%29+=+2+%2B+i\"\r\n" );
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document.write( "Multiply both sides by (x + iy)\r\n" );
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document.write( "\"1+=+%28x%2Biy%29%282+%2B+i%29\"\r\n" );
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document.write( "FOIL out the right side:\r\n" );
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document.write( "\"1+=+2x%2Bix%2B2iy+%2B+i%5E2y\"\r\n" );
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document.write( "\"1+=+2x%2Bix%2B2iy%2B%28-1%29y\"\r\n" );
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document.write( "\"1+=+2x%2Bix%2B2iy-y\"\r\n" );
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document.write( "Set the real terms on the left equal to the real terms on the right:\r\n" );
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document.write( "\"1=2x-y\"\r\n" );
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document.write( "Set the imaginary terms on the left equal to the imaginary terms on\r\n" );
document.write( "the right (there aren't any on the left so we use 0):\r\n" );
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document.write( "\"0=ix%2B2iy\"\r\n" );
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document.write( "divide through by i\r\n" );
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document.write( "\"0=x%2B2y\"\r\n" );
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document.write( "Solve the system:\r\n" );
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document.write( "\"system%281=2x-y%2C0=x%2B2y%29\"\r\n" );
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document.write( "Solve the first equation for y\r\n" );
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document.write( "\"y=2x-1\"\r\n" );
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document.write( "Substitute in the 2nd equation of the system:\r\n" );
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document.write( "\"0=x%2B2%282x-1%29\"\r\n" );
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document.write( "Distribute:\r\n" );
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document.write( "\"0=x%2B4x-2\"\r\n" );
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document.write( "Combine terma:\r\n" );
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document.write( "\"0=5x-2\"\r\n" );
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document.write( "Add 2 to both sides:\r\n" );
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document.write( "\"2=5x\"\r\n" );
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document.write( "Divide both sides by 5\r\n" );
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document.write( "\"2%2F5=x\"\r\n" );
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document.write( "Substitute for x in\r\n" );
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document.write( "\"y=2x-1\"\r\n" );
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document.write( "\"y=2%282%2F5%29-1\"\r\n" );
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document.write( "\"y=4%2F5-1\"\r\n" );
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document.write( "Multiple through by 5\r\n" );
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document.write( "\"5y=4-5\"\r\n" );
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document.write( "\"5y=-1\"\r\n" );
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document.write( "Divide both sides by 5\r\n" );
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document.write( "\"y=-1%2F5\" \r\n" );
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document.write( "Edwin

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