document.write( "Question 890275: Find the real part of 1 + z^2 *z \n" ); document.write( "
Algebra.Com's Answer #538902 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Did you mean\r\n" );
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document.write( "(1 + z²)z or 1+z²z?\r\n" );
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document.write( "If you meant (1 + z²)z, then let z = x + yi where x and y are real\r\n" );
document.write( "(1 + z²)z\r\n" );
document.write( "[1 + (x+yi)²](x+yi)\r\n" );
document.write( "[1 + x²+2xyi+y²i²](x+yi)\r\n" );
document.write( "Change i² to -1\r\n" );
document.write( "[1 + x²+2xyi+y²(-1)](x+yi)\r\n" );
document.write( "(1 + x²+2xyi-y²)(x+yi)\r\n" );
document.write( "Separate real terms from imaginary terms\r\n" );
document.write( "[(1+x²-y²)+2xyi](x+yi)\r\n" );
document.write( "USE FOIL:\r\n" );
document.write( "(1+x²-y²)x+(1+x²-y²)yi+2x²yi+2xy²i²\r\n" );
document.write( "x+x³-xy²+yi+x²yi-y³i+2x²yi+2xy²(-1)\r\n" );
document.write( "Change i² to -1\r\n" );
document.write( "x+x³-xy²+yi+x²yi-y³i+2x²yi-2xy²\r\n" );
document.write( "Separate real terms from imaginary terms\r\n" );
document.write( "(x+x³-xy²-2xy²)+(yi+x²yi-y³i+2x²yi)\r\n" );
document.write( "Combine like terms:\r\n" );
document.write( "(x+x³-3xy²)+(yi+3x²yi-y³i)\r\n" );
document.write( "Factor out i:\r\n" );
document.write( "(x+x³-3xy²)+(y+3x²y-y³)i\r\n" );
document.write( "Factor out common factors:\r\n" );
document.write( "x(1+x²-3y²)+y(1+3x²-y²)i\r\n" );
document.write( "So the real part is x(1+x²-3y²)\r\n" );
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document.write( "If you meant 1+z²z\r\n" );
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document.write( "1+z²z\r\n" );
document.write( "1+z³\r\n" );
document.write( "(1+z)(1-z+z²)\r\n" );
document.write( "(1+x+yi)[1-(x+yi)+(x+yi)²]\r\n" );
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document.write( "Go through that just as I did above and get:\r\n" );
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document.write( "x³-3xy²+1+(3x²y-y³)i\r\n" );
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document.write( "and the real part is x³-3xy²+1\r\n" );
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document.write( "Edwin
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