SOLUTION: 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? (Th

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: 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? (Th      Log On


   

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.)
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2Bi%29%2F%281%2B3i%29
Multiply numerator and denominator by complex conjugate:
%28%282%2Bi%29%281-3i%29%29%2F%28%281%2B3i%29%281-3i%29%29
%282-5i%2B3%29%2F%281%2B9%29
%285-5i%29%2F10
%281-i%29%2F2
So you did this right. And yes, you can distribute the denominator if you want to:
1%2F2-i%2F2 is also correct.
Good Luck,
tutor_paul@yahoo.com