document.write( "Question 78944: I need to find the quotient for 2+i over 1+3i. I know about multiplying by the conjugate, and I get 5-5i over 10, which simplifies to 1-i over 2. Is this the same as 1/2-1/2 i? (This is not a textbook problem, rather it is a take-home test. My teacher said we could use the internet.) \n" ); document.write( "

Algebra.Com's Answer #56666 by tutor_paul(519) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%282%2Bi%29%2F%281%2B3i%29\"$
\n" ); document.write( "Multiply numerator and denominator by complex conjugate:
\n" ); document.write( " $\"%28%282%2Bi%29%281-3i%29%29%2F%28%281%2B3i%29%281-3i%29%29\"$
\n" ); document.write( " $\"%282-5i%2B3%29%2F%281%2B9%29\"$
\n" ); document.write( " $\"%285-5i%29%2F10\"$
\n" ); document.write( " $\"%281-i%29%2F2\"$
\n" ); document.write( "So you did this right. And yes, you can distribute the denominator if you want to:
\n" ); document.write( " $\"1%2F2-i%2F2\"$ is also correct.
\n" ); document.write( "Good Luck,
\n" ); document.write( "tutor_paul@yahoo.com \n" ); document.write( "

\n" );