Answer
$\frac{84}{169}+\frac{35}{169}i$
Work Step by Step
$$\frac{7i}{(3+2i)^2}$$
Simplifying the denominator:
$$\frac{7i}{9+12i+4(-1)}=\frac{7i}{5+12i}$$
Rationalizing:
$$\frac{7i}{5+12i}\cdot \frac{5-12i}{5-12i}=\frac{35i-84(-1)}{25-144(-1)}=\frac{84+35i}{169}$$
Rearranging:
$$\frac{84}{169}+\frac{35}{169}i$$
