document.write( "Question 1207779: Let z and w be complex numbers such that |z| = |w| = 1 and zw is not equal to -1.\r
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Algebra.Com's Answer #845864 by mccravyedwin(407)\"\" \"About 
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Let z and w be complex numbers such that |z| = |w| = 1 and zw is not equal to -1.
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document.write( "where x,y,u,v are real numbers.\r\n" );
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document.write( "\"abs%28z%29=1\"\r\n" );
document.write( "\"sqrt%28x%5E2%2By%5E2%29=1\"\r\n" );
document.write( "\"x%5E2%2By%5E2=1\"\r\n" );
document.write( "\"x%5E2-%28-y%5E2%29=1\"\r\n" );
document.write( "\"x%5E2-%28-1%2Ay%5E2%29=1\"\r\n" );
document.write( "\"x%5E2-%28i%5E2y%5E2%29=1\"\r\n" );
document.write( "\"%28x-i%2Ay%29%28x%2Bi%2Ay%29=1\"\r\n" );
document.write( "\"x-i%2Ay=1%2F%28x%2Bi%2Ay%29\"\r\n" );
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\n" ); document.write( "(b) Prove that ={z + w}/{zw + 1} is a real number.
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document.write( "\"%28z+%2B+w%29%2F%28z%2Aw+%2B+1%29\"\r\n" );
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document.write( "Multiply numerator and denominator by the sum of the reciprocals of z and w:\r\n" );
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document.write( "\"%28z+%2B+w%29%2F%28z%2Aw+%2B+1%29\"\"%22%22%2A%22%22\"\"%281%2Fz+%2B+1%2Fw%29%2F%281%2Fz+%2B+1%2Fw%29\"\r\n" );
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document.write( "\"%281%2Bw%2Aexpr%281%2Fz%29%2Bz%2Aexpr%281%2Fw%29%2B1%29%2F%28w%2Bz%2B1%2Fz%2B1%2Fw%29\"\r\n" );
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document.write( "and since we have proved in part (a) that their reciprocals are their\r\n" );
document.write( "conjugates,\r\n" );
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document.write( "The imaginary terms cancel, and we have:\r\n" );
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document.write( "\"%282%2Bu%2Av%2Bx%2Au%29%2F%282%2Au%2B2%2Ax%29\"\r\n" );
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document.write( "which is real since 2,u,v,x,y are all real.\r\n" );
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document.write( "Edwin
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