In order to simplify this, you need to make sure ii isn't in the denominator (or bottom) of the fraction. To do this, multiply both the numerator and denominator by the conjugate of 3-2i3−2i, which is 3+2i3+2i. When doing this, make sure to use the FOIL method:
1)
((8+6i) * (3+2i))/((3-2i) * (3+2i))(8+6i)⋅(3+2i)(3−2i)⋅(3+2i)
2)
(24+16i+18i-12)/(9+6i-6i-4i^2)24+16i+18i−129+6i−6i−4i2
Since ii equals sqrt(-1)√−1, i^2i2 equals -1−1.
3)
(12+34i)/(9+4)12+34i9+4
4)
(12+34i)/(13)12+34i13