document.write( "Question 979594: Any help would be appreciated with this.\r
\n" ); document.write( "\n" ); document.write( "If s and t are two complex numbers, prove the following.\r
\n" ); document.write( "\n" ); document.write( "a) |s+t|^2=|s|^2+|t|^2+(st*+s*t)\r
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\n" ); document.write( "\n" ); document.write( "|s|^2+|t|^2+(st*+s*t)
\n" ); document.write( "=ss*+tt*+st*+s*t
\n" ); document.write( "Using s=a+bi and t=c+di
\n" ); document.write( "=a^2+b^2+c^2+d^2+2ac+2bd\r
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\n" ); document.write( "\n" ); document.write( "|s+t|^2 = a^2+2abi-b2+2ac+2bci+2adi-2bd+c^2+2cdi-d^2\r
\n" ); document.write( "\n" ); document.write( "Which seems quite wrong. \n" ); document.write( "

Algebra.Com's Answer #600888 by Edwin McCravy(20059) $\"\"$ $\"About$

You can put this solution on YOUR website!
If s and t are two complex numbers, prove the following.
\n" ); document.write( "|s+t|^2 = a^2+2abi-b2+2ac+2bci+2adi-2bd+c^2+2cdi-d^2
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document.write( "You did that wrong.  add s=a+bi and t=c+di before you find the magnitude\r\n" );
document.write( "or absolute value:\r\n" );
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document.write( "|s+t|² = |(a+bi)+(c+di)|² = |(a+c)+(b+d)i| = (a+c)²+(b+d)² = \r\n" );
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document.write( "a²+2ac+c²+b²+2bd+d² \r\n" );
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document.write( "Then when you do the other side:\r\n" );
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document.write( "|s|²+|t|²+(st*+s*t) = a²+b²+c²+d²+(a+bi)(c-di)+(a-bi)(c+di) = \r\n" );
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document.write( "a²+b²+c²+d²+ac-adi+bci+bd+ac+adi-bci+bd = a²+b²+c²+d²+2ac+2bd\r\n" );
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document.write( "and they are equal.\r\n" );
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document.write( "Edwin

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