document.write( "Question 1160752: Show that z^n +(complex conjugate of z)^n is always real for integer n. \n" ); document.write( "
Algebra.Com's Answer #784185 by math_helper(2461)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "x = a+bi = \"Me%5E%28i%2Atheta%29\"
\n" ); document.write( "x_ = a-bi = \"Me%5E%28-i%2Atheta%29\"\r
\n" ); document.write( "\n" ); document.write( "(x_ is complex conjugate of x)\r
\n" ); document.write( "\n" ); document.write( "where M=\"sqrt%28a%5E2%2Bb%5E2%29\" and \"theta+=+tan%5E-1%28b%2Fa%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5En+\" =
\n" ); document.write( "\"x_%5En+\" =
\n" ); document.write( "= \"+M%5En%2Acos%28theta%2An%29+-+i%2AM%5En%2Asin%28theta%2An%29+\"\r
\n" ); document.write( "\n" ); document.write( " = \"+blue%282%2AM%5En%2Acos%28theta%2An%29%29++\"\r
\n" ); document.write( "\n" ); document.write( "Notice \"+blue%282%2AM%5En%2Acos%28theta%2An%29%29++\" has no imaginary component, hence it is strictly real.\r
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