document.write( "Question 24527: Hi, can you show me how to solve a problem like this one?
\n" ); document.write( "Find Multiplicative Inverse.
\n" ); document.write( "-i
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\n" ); document.write( "3+5i \r
\n" ); document.write( "\n" ); document.write( "Is the answer just 3-5i ????
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\n" ); document.write( "please help me, thanks
\n" ); document.write( "----justin \n" ); document.write( "
Algebra.Com's Answer #13065 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
Hi, can you show me how to solve a problem like this one?\r\n" );
document.write( "  Find Multiplicative Inverse.\r\n" );
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document.write( "      -i\r\n" );
document.write( "     -----\r\n" );
document.write( "      3+5i\r\n" );
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document.write( "Is the answer just 3-5i     ????\r\n" );
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document.write( "                    i         \r\n" );
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document.write( "No.  You do invert it, but you don't change any signs yet.\r\n" );
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document.write( "It's simply the original problem inverted without changing any\r\n" );
document.write( "signe\r\n" );
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document.write( "3 + 5i\r\n" );
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document.write( "  -i \r\n" );
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document.write( "However that's not finished.\r\n" );
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document.write( "You write the denominator as 0 - 1i\r\n" );
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document.write( "3 + 5i\r\n" );
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document.write( "0 - 1i\r\n" );
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document.write( "Then you form the conjugate of the denominator, 0 - 1i.\r\n" );
document.write( "(This is the only time where you change the sign of the second term.)\r\n" );
document.write( "The conjugate of 0 - 1i is 0 + 1i.  So you form the fraction by putting\r\n" );
document.write( "that over itself, so that it just equals 1\r\n" );
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document.write( "0 + 1i\r\n" );
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document.write( "0 + 1i\r\n" );
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document.write( "Then you multiply \r\n" );
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document.write( "3 + 5i\r\n" );
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document.write( "0 - 1i\r\n" );
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document.write( "by that:\r\n" );
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document.write( "3 + 5i   0 + 1i\r\n" );
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document.write( "0 - 1i   0 + 1i\r\n" );
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document.write( "Use FOIL in numerator and denominator\r\n" );
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document.write( "3·0 + 3·1i + 5i·0 + 5i2\r\n" );
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document.write( "0·0 + 0·1i - 0·1i - 1i2\r\n" );
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document.write( " 3i + 5i2\r\n" );
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document.write( "  -1i2\r\n" );
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document.write( "Now we replace i2 by -1\r\n" );
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document.write( " 3i + 5(-1)\r\n" );
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document.write( "   -1(-1)\r\n" );
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document.write( " 3i - 5\r\n" );
document.write( "--------\r\n" );
document.write( "    1\r\n" );
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document.write( "or just\r\n" );
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document.write( " 3i - 5\r\n" );
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document.write( "It is customary to write the \"i\" part last, so the answer is\r\n" );
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document.write( "-5 + 3i\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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