document.write( "Question 65436This question is from textbook An Incremental Development
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Algebra.Com's Answer #45969 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "(-3i2 + 4i - 5)Ö-9 - 4 + 5i3\r\n" );
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document.write( "Combine the -9 and the -4 under the radical\r\n" );
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document.write( "(-3i2 + 4i - 5)Ö-13 + 5i3\r\n" );
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document.write( "Since  i2 = -1 and i3 = -i, replace those\r\n" );
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document.write( "( -3(-1) + 4i - 5 )Ö-13 + 5(-i)\r\n" );
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document.write( "( 3 + 4i - 5)Ö-13 - 5i\r\n" );
document.write( "            ________  \r\n" );
document.write( "( -2 + 4i )Ö-13 - 5i\r\n" );
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document.write( "Assume this equals to the complex number A + Bi, where\r\n" );
document.write( "A and B are real numbers\r\n" );
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document.write( "(-2 + 4i)Ö-13 - 5i = A + Bi\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "            ________  \r\n" );
document.write( "(-2 + 4i)2(Ö-13 - 5i)2 = (A + Bi)2\r\n" );
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document.write( "(4 - 16i + 16i2)(-13 - 5i) = A2 + 2ABi + B2i2\r\n" );
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document.write( "Replace the i2's by -1\r\n" );
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document.write( "( 4 - 16i + 16(-1) )(-13 - 5i) = A2 + 2ABi + B2(-1)\r\n" );
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document.write( "( 4 - 16i - 16 )(-13 - 5i) = A2 + 2ABi - B2\r\n" );
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document.write( "(-12 - 16i)(-13 - 5i) = A² + 2ABi - B2\r\n" );
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document.write( "156 + 60i + 208i + 80i2 = A2 + 2ABi - B2\r\n" );
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document.write( "Replace the i2 by -1\r\n" );
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document.write( "156 + 60i + 208i + 80(-1) = A2 + 2ABi - B2\r\n" );
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document.write( "156 + 60i + 208i - 80 = A2 + 2ABi - B2\r\n" );
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document.write( "76 + 268i = A2 + 2ABi - B2\r\n" );
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document.write( "The real numbers on the left must equal the real\r\n" );
document.write( "numbers on the right, so\r\n" );
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document.write( "76 = A2 - B2\r\n" );
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document.write( "A2 - B2 = 76\r\n" );
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document.write( "The imaginary numbers on the left must equal the\r\n" );
document.write( "imaginary numbers on the right, so\r\n" );
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document.write( "268i = 2ABi\r\n" );
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document.write( "Dividing thru by 2i\r\n" );
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document.write( "134 = AB\r\n" );
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document.write( " AB = 134\r\n" );
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document.write( "So we have this system of equations:\r\n" );
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document.write( "A2 - B2 = 76\r\n" );
document.write( "     AB = 134\r\n" );
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document.write( "To make things easier square the second equation\r\n" );
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document.write( "    A2B2 = 17956\r\n" );
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document.write( "Solve it for B2\r\n" );
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document.write( "      B2 = 17956/A2\r\n" );
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document.write( "Substitute for B2 in the first equation\r\n" );
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document.write( "A2 - 17956/A2 = 76\r\n" );
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document.write( "A4 - 17956 = 76A2\r\n" );
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document.write( "A4 - 76A2 - 17956 = 0\r\n" );
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document.write( "Solve that for A2 by the quadratic formula\r\n" );
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document.write( "A2 = 177.2838828, A2 = -101.2838828\r\n" );
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document.write( "But since A is real A2 is positive so we discard\r\n" );
document.write( "the negative value\r\n" );
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document.write( "A2 = 177.2838828\r\n" );
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document.write( "Taking square roots:\r\n" );
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document.write( "A = ±13.31479939\r\n" );
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document.write( "Substitute 177.2839928 for A2 in\r\n" );
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document.write( "A2 - B2 = 76\r\n" );
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document.write( "177.2838828 - B2 = 76\r\n" );
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document.write( "177.2838828 - 76 = B2\r\n" );
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document.write( "101.2838828 = B2\r\n" );
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document.write( "B2 = 101.2838828\r\n" );
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document.write( "Taking square roots:\r\n" );
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document.write( "B = ± 10.06398941\r\n" );
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document.write( "So we get four solutions:\r\n" );
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document.write( "A + Bi =  13.31479939 + 10.06398941i\r\n" );
document.write( "A + Bi =  13.31479939 - 10.06398941i\r\n" );
document.write( "A + Bi = -13.31479939 + 10.06398941i\r\n" );
document.write( "A + Bi = -13.31479939 - 10.06398941i\r\n" );
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document.write( "However we can eliminate two of these because\r\n" );
document.write( "of the equation\r\n" );
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document.write( "     AB = 134\r\n" );
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document.write( "since 134 is a positive number, which means\r\n" );
document.write( "that A and B must have the same sign.  This\r\n" );
document.write( "only leaves the two solutions:\r\n" );
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document.write( "A + Bi =  13.31479939 + 10.06398941i\r\n" );
document.write( "A + Bi = -13.31479939 - 10.06398941i\r\n" );
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document.write( "Both those are correct answers because\r\n" );
document.write( "there are two complex imaginary square\r\n" );
document.write( "roots of a complex imaginary number.\r\n" );
document.write( "The original problem contains\r\n" );
document.write( "a square root of a complex number, thus\r\n" );
document.write( "we expect two answers.\r\n" );
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document.write( "Edwin
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