document.write( "Question 1123289: Show that ǀz1 + z2ǀ˄2 + ǀz1 - z2ǀ˄2= 2ǀz1ǀ˄2 + 2ǀz2ǀ˄2 \n" ); document.write( "

Algebra.Com's Answer #739649 by ikleyn(52797) $\"\"$ $\"About$

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document.write( "Let Z1 be the complex conjugate to z1, ans Let Z2 be the complex conjugate to z2.\r\n" );
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document.write( "Then\r\n" );
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document.write( "|z1 + z2|^2 + |z1 - z2|^2 = (z1 + z2)*(Z1 + Z2) + (z1 - z2)*(Z1 - Z2) = \r\n" );
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document.write( "                          = z1*Z1 + z2*Z1 + z1*Z2 + z2*Z2 + z1*Z1 - z2*Z1 - z1*Z2 + z2*Z2 = \r\n" );
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document.write( "                          = 2*z1*Z1 + 2*z2*Z2  = 2*|z1|^2 + 2*|z2|^2.\r\n" );
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document.write( "QED.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Simply another proof.\r
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