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