document.write( "Question 394152: 
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document.write( "How do you rewrite each quotient in the form a+bi?\r\n" );
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document.write( "  2\r\n" );
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document.write( " 3+i\r\n" );
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Algebra.Com's Answer #279649 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
How do you rewrite each quotient in the form a+bi?
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document.write( "  2\r\n" );
document.write( "-----\r\n" );
document.write( " 3+i\r\n" );
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document.write( "Multiply by the conjugate of the bottom, which is formed by\r\n" );
document.write( "changing the sign of the term with \"i\" (leaving the sign of\r\n" );
document.write( "the term without the \"i\").\r\n" );
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document.write( "The conjugate of 3+i is 3-i.  So we put that over itself \"%283-i%29%2F%283-i%29\"\r\n" );
document.write( "so it will equal 1 and therefore not change the numerical value of the\r\n" );
document.write( "given expression:\r\n" );
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document.write( "  2      3-i \r\n" );
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document.write( " 3+i     3-i\r\n" );
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document.write( "Then multiply out the top and bottom, distributing on top and\r\n" );
document.write( "using FOIL on the bottom:\r\n" );
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document.write( "    6-2i       \r\n" );
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document.write( " 9-3i+3i-i²\r\n" );
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document.write( "Cancel the two middle terms on the bottom:\r\n" );
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document.write( "  6-2i       \r\n" );
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document.write( "  9-i²\r\n" );
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document.write( "Replace i² by (-1)\r\n" );
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document.write( "   6-2i       \r\n" );
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document.write( "  9-(-1)\r\n" );
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document.write( "   6-2i       \r\n" );
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document.write( "   9+1\r\n" );
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document.write( "   6-2i       \r\n" );
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document.write( "    10\r\n" );
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document.write( "Factor 2 out of the top:\r\n" );
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document.write( "  2(3-i)       \r\n" );
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document.write( "    10\r\n" );
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document.write( "Cancel the 2 into the 10 getting 5\r\n" );
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document.write( " 3-i\r\n" );
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document.write( "  5\r\n" );
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document.write( "Make two fractions:\r\n" );
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document.write( " 3     i\r\n" );
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document.write( " 5     5\r\n" );
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document.write( "But you can write the last term as one-fifth of i\r\n" );
document.write( "since dividing by 5 is the same as multiplying by \"1%2F5\"\r\n" );
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document.write( "Answer:  \"3%2F5-expr%28i%2F5%29i\"\r\n" );
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document.write( "Edwin
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