document.write( "Question 1106840: zz*+3(z-z*)=13+12i \n" ); document.write( "
Algebra.Com's Answer #721821 by Edwin McCravy(20055)\"\" \"About 
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zz*+3(z-z*) = 13+12i\r\n" );
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document.write( "Substitute x+yi for z and x-yi for conjugate z*,\r\n" );
document.write( "where x and y are real.\r\n" );
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document.write( "(x+yi)(x-yi)+3[(x+yi)-(x-yi)] = 13+12i\r\n" );
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document.write( "Simplify the left side:\r\n" );
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document.write( "x²-y²i²+3[x+yi-x+yi] = 13+12i\r\n" );
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document.write( "Simplify using the fact that i² = -1\r\n" );
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document.write( "x²-y²(-1)+3[2yi] = 13+12i\r\n" );
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document.write( "x²+y²+6yi = 13+12i\r\n" );
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document.write( "Set the sum of the two real-numbered terms on the \r\n" );
document.write( "left side, x²+y² equal to the real term, 13, on \r\n" );
document.write( "the right side:\r\n" );
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document.write( "x²+y² = 13  <--equation #1\r\n" );
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document.write( "Set the sum of the two imaginary term on the \r\n" );
document.write( "left side, 6yi equal to the imaginary term, 12i, on \r\n" );
document.write( "the right side:\r\n" );
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document.write( "6yi = 12i\r\n" );
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document.write( "Divide both sides by 6i\r\n" );
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document.write( "y = 2\r\n" );
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document.write( "Substitute 2 for y in \r\n" );
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document.write( "x²+y² = 13\r\n" );
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document.write( "x²+2² = 13\r\n" );
document.write( " x²+4 = 13\r\n" );
document.write( "   x² = 9\r\n" );
document.write( "    x = ±3\r\n" );
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document.write( "We get two answers: \r\n" );
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document.write( "z = x+yi = ±3+2i\r\n" );
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document.write( "So the two answers are z = 3+2i and x = -3+2i \r\n" );
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document.write( "Edwin
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