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