document.write( "Question 65972: Hello! I'm having trouble with this equation because I don't know how to solve for \"k\". Here is the equation. \r
\n" ); document.write( "\n" ); document.write( "If 1+2i is a root of x^2-kx+6=0, find k.\r
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\n" ); document.write( "\n" ); document.write( "Sincerely,
\n" ); document.write( "Leanne Spence \n" ); document.write( "
Algebra.Com's Answer #46721 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Hello! I'm having trouble with this equation \r\n" );
document.write( "because I don't know how to solve for \"k\". \r\n" );
document.write( "Here is the equation. \r\n" );
document.write( "If 1+2i is a root of x^2-kx+6=0, find k. \r\n" );
document.write( "Can you help me out? \r\n" );
document.write( "Sincerely,\r\n" );
document.write( "Leanne Spence\r\n" );
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document.write( "Substitute 1+2i for x and solve for k:\r\n" );
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document.write( "                    x² - kx + 6 = 0\r\n" );
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document.write( "          (1+2i)² - k(1+2i) + 6 = 0\r\n" );
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document.write( "     (1+2i)(1+2i) - k - 2ik + 6 = 0\r\n" );
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document.write( "1 + 2i + 2i + 4i² - k - 2ik + 6 = 0\r\n" );
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document.write( "         7 + 4i + 4i² - k - 2ik = 0\r\n" );
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document.write( "Since i² = -1 replace i² by -1\r\n" );
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document.write( "       7 + 4i + 4(-1) - k - 2ik = 0\r\n" );
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document.write( "           7 + 4i - 4 - k - 2ik = 0\r\n" );
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document.write( "               3 + 4i - k - 2ik = 0\r\n" );
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document.write( "Get all the k terms on the right\r\n" );
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document.write( "                         3 + 4i = k + 2ik\r\n" );
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document.write( "Factor k out on the right\r\n" );
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document.write( "                         3 + 4i = k(1 + 2i)\r\n" );
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document.write( "Divide both sides by 1 + 2i\r\n" );
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document.write( "                         3 + 4i  \r\n" );
document.write( "                        -------- = k\r\n" );
document.write( "                         1 + 2i\r\n" );
document.write( "     \r\n" );
document.write( "To divide out the two complex numbers, \r\n" );
document.write( "multiply top and bottom by conjugate\r\n" );
document.write( "of bottom, 1 - 2i\r\n" );
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document.write( "                (3 + 4i)(1 - 2i)\r\n" );
document.write( "               ------------------ = k\r\n" );
document.write( "                (1 + 2i)(1 - 2i)\r\n" );
document.write( "                           \r\n" );
document.write( "               3 - 6i + 4i - 8i²\r\n" );
document.write( "             -------------------- = k\r\n" );
document.write( "               1 - 2i + 2i - 4i²\r\n" );
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document.write( "                    3 - 2i - 8i²\r\n" );
document.write( "                   -------------- = k\r\n" );
document.write( "                      1 - 4i²              \r\n" );
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document.write( "Replace i² by -1\r\n" );
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document.write( "                  3 - 2i - 8(-1)\r\n" );
document.write( "                 ---------------- = k\r\n" );
document.write( "                    1 - 4(-1) \r\n" );
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document.write( "                      3 - 2i + 8\r\n" );
document.write( "                     ------------ = k\r\n" );
document.write( "                         1 + 4\r\n" );
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document.write( "                         11 - 2i \r\n" );
document.write( "                        --------- = k\r\n" );
document.write( "                            5 \r\n" );
document.write( "or in A + Bi form in fractions\r\n" );
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document.write( "       k = (11/5) - (2/5)i\r\n" );
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document.write( "or in A + Bi form in decimals\r\n" );
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document.write( "       k = 2.2 - 0.4i \r\n" );
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document.write( "Edwin
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