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You should type as : x^4 = -3
\n" ); document.write( " Since -3 = 3*-1 = 3(cos pi + i sin pi)
\n" ); document.write( " Solve x^4 = 3(cos pi + i sin pi)
\n" ); document.write( " By De Mieve Law , we have x = 3^(1/4)(cos pi/4 + i sin pi/4)
\n" ); document.write( " = 3^(1/4)(sqrt(2)/2 + i sqrt(2)/2)
\n" ); document.write( "
\n" ); document.write( " This is one of the 4th (primitive) root of -3.\r
\n" ); document.write( "\n" ); document.write( " Better and complete general solutions as:
\n" ); document.write( " x^4 = 3(cos (2k pi +pi) + i sin (2k pi +pi)) for integer k
\n" ); document.write( " So, x = 3^(1/4)(cos (2k+1)pi/4 + i sin(2k+1)pi/4) where k =0,1,2,3
\n" ); document.write( " Hence, x = 3^(1/4)(sqrt(2)/2 + i sqrt(2)/2) (when k = 0)
\n" ); document.write( " or x = 3^(1/4)(cos 3pi/4 + i sin 3pi/4)
\n" ); document.write( " = 3^(1/4)(-sqrt(2)/2 + i sqrt(2)/2) (when k = 1)
\n" ); document.write( " or x = 3^(1/4)(cos 5pi/4 + i sin 5pi/4)
\n" ); document.write( " = 3^(1/4)(-sqrt(2)/2 - i sqrt(2)/2) (when k = 2)
\n" ); document.write( " or x = 3^(1/4)(cos 7pi/4 + i sin 7pi/4)
\n" ); document.write( " = 3^(1/4)(sqrt(2)/2 - i sqrt(2)/2) (when k = 3)
\n" ); document.write( "
\n" ); document.write( " For any integer n and complex number w=a+bi, the equation x^n = w
\n" ); document.write( " has n solutions.
\n" ); document.write( " By x^n = w = r(cos t + i sin t) where r = }w} and tan t = b/a
\n" ); document.write( " x = r^(1/n) cos ( 2pik + t)/n + i sin ( 2pik + t)/n , k=0,1,2,..,k-1\r
\n" ); document.write( "\n" ); document.write( " Kenny\r
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