document.write( "Question 1074213: (a+bi)^2=i \r
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Algebra.Com's Answer #688925 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"%28a%2Bbi%29%5E2=i+\"\r\n" );
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document.write( "\"%28a%2Bbi%29%28a%2Bbi%29=i+\"\r\n" );
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document.write( "\"a%5E2%2B2abi%2Bb%5E2i%5E2=i\"\r\n" );
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document.write( "Since i2 = -1\r\n" );
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document.write( "\"a%5E2%2B2abi%2Bb%5E2%28-1%29=i\"\r\n" );
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document.write( "\"a%5E2%2B2abi-b%5E2=i\"\r\n" );
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document.write( "Set the real part of the left side equal to the real\r\n" );
document.write( "part of the right side:\r\n" );
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document.write( "and\r\n" );
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document.write( "Set the imaginary part of the left side equal to the \r\n" );
document.write( "imaginary part of the right side:\r\n" );
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document.write( "\"a%5E2-b%5E2=0\"  and  \"2abi=i\"\r\n" );
document.write( "                      \"b=i%2F%282ai%29\"\r\n" );
document.write( "                      \"b=1%2F%282a%29\"\r\n" );
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document.write( "Substitute for b in\r\n" );
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document.write( "\"a%5E2-b%5E2=0\"\r\n" );
document.write( "\"a%5E2-%281%2F%282a%29%29%5E2=0\"\r\n" );
document.write( "\"a%5E2-1%2F%284a%5E2%29=0\"\r\n" );
document.write( "\"4a%5E4-1=0\"\r\n" );
document.write( "\"%282a%5E2-1%29%282a%5E2%2B1%29=0\"\r\n" );
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document.write( "\"2a%5E2-1=0\"; \"2a%5E2%2B1=01\"\r\n" );
document.write( "\"2a%5E2=1\";   \"2a%5E2=-1\"\r\n" );
document.write( "\"a%5E2=1%2F2\";  \"a%5E2=-1%2F2\"\r\n" );
document.write( "\"a=+%22%22+%2B-+sqrt%281%2F2%29%3B+++%7B%7B%7Ba%5E2=%22%22+%2B-+sqrt%28-1%2F2%29\"\r\n" );
document.write( "\"a=+%22%22+%2B-+1%2Fsqrt%282%29\"; \"a=%22%22+%2B-i%2Asqrt%281%2F2%29\"\r\n" );
document.write( "\"a=%22%22+%2B-+sqrt%282%29%2F2\"; ignore the imaginary value for a\r\n" );
document.write( "Substitute in:\r\n" );
document.write( "\"b=1%2F%282a%29\"\r\n" );
document.write( "\"b=1%2F%282%28%22%22+%2B-+sqrt%282%29%2F2%29%29\"\r\n" );
document.write( "\"b=1%2F%28cross%282%29%28%22%22+%2B-+sqrt%282%29%2Fcross%282%29%29%29\" \r\n" );
document.write( "\"b=1%2F%28%22%22+%2B-+sqrt%282%29%29\" \r\n" );
document.write( "\"b=%22%22+%2B-+sqrt%282%29%2F2\"\r\n" );
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document.write( "So there are two solutions:\r\n" );
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document.write( "\"a=%22%22+%2B-+sqrt%282%29%2F2\"; \"b=%22%22+%2B-+sqrt%282%29%2F2\"\r\n" );
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document.write( "One solution is where a and b are both positive,\r\n" );
document.write( "and the other solution is when they are both\r\n" );
document.write( "negative.\r\n" );
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document.write( "Edwin
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