Answer
$\frac{5}{13}+\frac{12}{13}i$
Work Step by Step
Step 1: $\frac{3+2i}{3-2i}\times\frac{3+2i}{3+2i}$
Step 2: $\frac{(3+2i)(3+2i)}{(3-2i)(3+2i)}$
Step 3: $\frac{3(3+2i)+2i(3+2i)}{3^{2}-(2i)^{2}}$
Step 4: $\frac{9+6i+6i+4i^{2}}{9-4i^{2}}$
Step 5: $\frac{9+12i+4(-1)}{9-4(-1)}$
Step 6: $\frac{9-4+12i}{13}$
Step 7: $\frac{5+12i}{13}$
Step 8: $\frac{5}{13}+\frac{12}{13}i$
