document.write( "Question 164498: What does the quotient equal?
\n" ); document.write( "\"%283%2Bi%29%2F%282-3i%29\" \n" ); document.write( "
Algebra.Com's Answer #121209 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
What does the quotient equal?
\n" ); document.write( "\"%283%2Bi%29%2F%282-3i%29\"
\n" ); document.write( "
\r\n" );
document.write( "Form the conjugate of the denominator:\r\n" );
document.write( "\r\n" );
document.write( "The denominator is \"2-3i\" so to form\r\n" );
document.write( "the conjugate we use the first term but\r\n" );
document.write( "we change the sign of the term in \"i\",\r\n" );
document.write( "so the conjugate of \"2-3i\" is \"2%2B3i\"\r\n" );
document.write( "Put that over itself. That is, we form the \r\n" );
document.write( "fraction \"%282%2B3i%29%2F%282%2B3i%29\" which is just \"1\" \r\n" );
document.write( "in value.\r\n" );
document.write( "\r\n" );
document.write( "Then we multiply the original expression by\r\n" );
document.write( "this:\r\n" );
document.write( "\r\n" );
document.write( "\"matrix%281%2C3%2C+%283%2Bi%29%2F%282-3i%29%2C+%22%D7%22+%2C+%282%2B3i%29%2F%282%2B3i%29+%29\"\r\n" );
document.write( "\r\n" );
document.write( "Put parentheses around everything:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Indicate the multiplication of numerators and denominators:\r\n" );
document.write( "\r\n" );
document.write( "\"%28%283%2Bi%29%282%2B3i%29%29%2F%28%282-3i%29%282%2B3i%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Use FOIL on the top and bottom:\r\n" );
document.write( "\r\n" );
document.write( "\"%286%2B9i%2B2i%2B3i%5E2%29%2F%284%2B6i-6i-9i%5E2%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%286%2B11i%2B3i%5E2%29%2F%284%2Bcross%286i%29-cross%286i%29-9i%5E2%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%286%2B11i%2B3i%5E2%29%2F%284-9i%5E2%29\"\r\n" );
document.write( "\r\n" );
document.write( "Now replace the \"i%5E2\"'s by \"-1\"\r\n" );
document.write( "\r\n" );
document.write( "\"%286%2B11i%2B3%28-1%29%29%2F%284-9%28-1%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%286%2B11i-3%29%2F%284%2B9%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%283%2B11i%29%2F13\"\r\n" );
document.write( "\r\n" );
document.write( "Make two fractions:\r\n" );
document.write( "\r\n" );
document.write( "\"3%2F13+%2B+11i%2F13\"\r\n" );
document.write( "\r\n" );
document.write( "To write it in the form \"A%2BBi\",\r\n" );
document.write( "\r\n" );
document.write( "\"3%2F13+%2B+11%2F13\"\"i\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );