What is 2+3i / 6+i simplified?

Question

This is for my pre-calc homework )':

Answer 1

When simplifying equations with "i" in the denominator, you must get it so that "i" is no longer in the denominator. You do this by multiplying the numerator and denominator by whatever will eliminate the "i" in the denominator. In this case we need to multiply top and bottom by 6-i:

(2+3i)(6-i)/(6+i)(6-i)=(12-2i+18i-3i²)/(36-6i+6i-i²)

                               =(12+16i-3(-1))/(36-(-1))

                               =(12+16i+3)/(36+1)

                               =(15+16i)/37