document.write( "Question 976172: COMPLEX NUMBER
\n" ); document.write( "If \"z+=+a%2Bbi\" and \"abs%28%28z-i%29%2F%28z%2B2%2Bi%29%29=3\", show that \"8a%5E2+%2B+8b%5E2+%2B+36a+%2B20b+%2B44+=0\"\r
\n" ); document.write( "\n" ); document.write( "Thanks. \n" ); document.write( "
Algebra.Com's Answer #597826 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
COMPLEX NUMBER
\n" ); document.write( "If \"z+=+a%2Bbi\" and \"abs%28%28z-i%29%2F%28z%2B2%2Bi%29%29=3\", show that \"8a%5E2+%2B+8b%5E2+%2B+36a+%2B20b+%2B44+=0\"\r
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "\"abs%28%28z-i%29%2F%28z%2B2%2Bi%29%29\"\"%22%22=%22%22\"\"3\"\r\n" );
document.write( "\r\n" );
document.write( "\"abs%28+%28%28a%2Bbi%29-i%29%2F%28%28a%2Bbi%29%2B2%2Bi%29%29\"\"%22%22=%22%22\"\"3\"\r\n" );
document.write( "\r\n" );
document.write( "\"abs%28%28a%2Bbi-i%29%2F%28a%2Bbi%2B2%2Bi%29%29\"\"%22%22=%22%22\"\"3\"\r\n" );
document.write( "\r\n" );
document.write( "\"abs%28%28a%2B%28bi-i%29%29%2F%28a%2B2%2B%28bi%2Bi%29%29%29\"\"%22%22=%22%22\"\"3\"\r\n" );
document.write( "\r\n" );
document.write( "\"abs%28%28a%2B%28b-1%29i%29%2F%28%28a%2B2%29%2B%28b%2B1%29i%29%29\"\"%22%22=%22%22\"\"3\"\r\n" );
document.write( "\r\n" );
document.write( "\"sqrt%28a%5E2%2B%28b-1%29%5E2%29%2Fsqrt%28%28a%2B2%29%5E2%2B%28b%2B1%29%5E2%29\"\"%22%22=%22%22\"\"3\"\r\n" );
document.write( "\r\n" );
document.write( "Square both sides:\r\n" );
document.write( "\r\n" );
document.write( "\"%28a%5E2%2B%28b-1%29%5E2%29%2F%28%28a%2B2%29%5E2%2B%28b%2B1%29%5E2%29\"\"%22%22=%22%22\"\"9\"\r\n" );
document.write( "\r\n" );
document.write( "\"a%5E2%2B%28b-1%29%5E2\"\"%22%22=%22%22\"\"9%28%28a%2B2%29%5E2%2B%28b%2B1%29%5E2%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"a%5E2%2B%28b-1%29%5E2\"\"%22%22=%22%22\"\"9%28a%2B2%29%5E2%2B9%28b%2B1%29%5E2%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"a%5E2-9%28a%2B2%29%5E2\"\"%22%22=%22%22\"\"9%28b%2B1%29%5E2-%28b-1%29%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "Both sides are differences of squares, so factor:\r\n" );
document.write( "\r\n" );
document.write( "\"%28a-3%28a%2B2%29%5E%22%22%29%28a%2B3%28a%2B2%29%5E%22%22%29\"\"%22%22=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28a-3%28a%2B2%29%29%28a%2B3%28a%2B2%29%29\"\"%22%22=%22%22\"\"%283%28b%2B1%29-%28b-1%29%29%283%28b%2B1%29%2B%28b-1%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28a-3a-6%29%28a%2B3a%2B6%29\"\"%22%22=%22%22\"\"%283b%2B3-b%2B1%29%283b%2B3%2Bb-1%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28-2a-6%29%284a%2B6%29\"\"%22%22=%22%22\"\"%282b%2B4%29%284b%2B2%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28-2%28a%2B3%29%5E%22%22%29%282%282a%2B3%29%5E%22%22%29\"\"%22%22=%22%22\"\"%282%28b%2B2%29%5E%22%22%29%282%282b%2B1%29%5E%22%22%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"-4%28a%2B3%29%282a%2B3%29\"\"%22%22=%22%22\"\"4%28b%2B2%29%282b%2B1%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"-%28a%2B3%29%282a%2B3%29\"\"%22%22=%22%22\"\"%28b%2B2%29%282b%2B1%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"-%282a%5E2%2B9a%2B9%29\"\"%22%22=%22%22\"\"2b%5E2%2B5b%2B2\"\r\n" );
document.write( "\r\n" );
document.write( "\"-2a%5E2-9a-9\"\"%22%22=%22%22\"\"2b%5E2%2B5b%2B2\"\r\n" );
document.write( "\r\n" );
document.write( "\"-2a%5E2-9a-2b%5E2-5b-11\"\"%22%22=%22%22\"\"0\"\r\n" );
document.write( "\r\n" );
document.write( "\"2a%5E2%2B9a%2B2b%5E2%2B5b%2B11\"\"%22%22=%22%22\"\"0\"\r\n" );
document.write( "\r\n" );
document.write( "If you swap 2nd and 3rd terms and multiply through by 4, you get \r\n" );
document.write( "\r\n" );
document.write( "\"8a%5E2+%2B+8b%5E2+%2B+36a+%2B20b+%2B44\"\"%22%22=%22%22\"\"0\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
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