document.write( "Question 853804: I have a Problem with complex Numbers
\n" ); document.write( "suppose we have a complex Number Z=x+iy
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\n" ); document.write( "Z*Z+(1+i)*Z+(5-i4)=0. \n" ); document.write( "
Algebra.Com's Answer #514322 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Z² + (1+i)Z + (5-i4) = 0\r\n" );
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document.write( "That's a quadratic in Z.  Use the quadratic formula:\r\n" );
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document.write( "\"Z+=+%28-%281%2Bi%29+%2B-+sqrt%28%281%2Bi%29%5E2-4%281%29%285-i4%29%29%29%2F%282%281%29%29+\"\r\n" );
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document.write( "\"Z+=+%28-1-i+%2B-+sqrt%28%281%2B2i%2Bi%5E2%29-4%285-i4%29%29%29%2F2+\"\r\n" );
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document.write( "\"Z+=+%28-1-i+%2B-+sqrt%281%2B2i%2Bi%5E2-20%2B16i%29%29%29%2F2+\"\r\n" );
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document.write( "\"Z+=+%28-1-i+%2B-+sqrt%281%2B18i%2Bi%5E2-20%29%29%29%2F2+\"\r\n" );
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document.write( "Replace i² by (-1)\r\n" );
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document.write( "\"Z+=+%28-1-i+%2B-+sqrt%281%2B18i%2B%28-1%29-20%29%29%29%2F2+\"\r\n" );
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document.write( "\"Z+=+%28-1-i+%2B-+sqrt%281%2B18i-1-20%29%29%29%2F2+\"\r\n" );
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document.write( "Now we have to find the square root by DeMoivre's theorem:\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C-20%2B18i%29%5E%281%2F2%29%29\"\r\n" );
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document.write( "Put -20+18i in polar form\r\n" );
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document.write( "\"r=sqrt%28%28-20%29%5E2%2B18%5E2%29=sqrt%28400%2B324%29=sqrt%28724%29\"\r\n" );
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document.write( "\"theta=tan%5E%22-1%22%2818%2F%28-20%29%29=tan%5E%22-1%22%28-0.9%29\"\r\n" );
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document.write( "\"-20%2B18i+=+sqrt%28724%29%2Acis%28tan%5E%22-1%22%28-0.9%29%29\"\r\n" );
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document.write( "\"%22%22=%22%22\"\r\n" );
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document.write( "root(4,724)cis(expr(tan^\"-1\"(-0.9))/2)\r\n" );
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document.write( "or decimal approximation (and you can get it immediately with a TI-84\r\n" );
document.write( "straight from the original equation):\r\n" );
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document.write( "Z = .4291964334+1.92144709i,  -1.429196433-2.92144709i\r\n" );
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document.write( "Edwin
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