Answer
$\frac{3}{7}-\frac{2}{7}i$
Work Step by Step
Step 1: $\frac{2+3i}{7i}$
Step 2: $\frac{2+3i}{7i}\times\frac{i}{i}$
Step 3: $\frac{i(2+3i)}{7i^{2}}$
Step 4: As $i^{2}=-1$, we get $\frac{2i+3(-1)}{7(-1)}$.
Step 5: $\frac{2i-3}{-7}$
Step 6: $\frac{2i}{-7}+\frac{(-3)}{(-7)}$
Step 7: $\frac{-2i}{7}+\frac{3}{7}$
Step 8: $\frac{3}{7}-\frac{2}{7}i$