Answer
$\frac{1}{5}+\frac{3}{5}i$
Work Step by Step
Step 1: $\frac{2i}{3+i}\times\frac{3-i}{3-i}$
Step 2: $\frac{2i(3-i)}{(3+i)(3-i)}$
Step 3: $\frac{6i-2i^{2}}{3^{2}-i^{2}}$
Step 4: $\frac{6i-2(-1)}{3^{2}-(-1)}$
Step 5: $\frac{6i+2}{9+1}$
Step 6: $\frac{2+6i}{10}$
Step 7: $\frac{2(1+3i)}{10}$
Step 8: $\frac{(1+3i)}{5}$
Step 9: $\frac{1}{5}+\frac{3}{5}i$
