Answer
(c) $\frac{14}{25}+\frac{23}{25}i$
Work Step by Step
$\frac{5+2i}{4-3i}$
=$\frac{5+2i}{4-3i}\times\frac{4+3i}{4+3i}$
=$\frac{5(4+3i)+2i(4+3i)}{4^{2}-(3i)^{2}}$
=$\frac{20+15i+8i+6i^{2}}{16-9i^{2}}$
=$\frac{20+15i+8i+6(-1)}{16-9(-1)}$
=$\frac{14+23i}{25}$
=$\frac{14}{25}+\frac{23}{25}i$