Answer
$\frac{11}{13}+\frac{10}{13}i$
Work Step by Step
Given: $$ \frac{1+4i}{3+2i}$$
Multiply numerator and denominator by the conjugate of the denominator, as follows:
$$ \frac{1+4i}{3+2i}=\frac{1+4i}{3+2i}\times\frac{3-2i}{3-2i}$$
Since, $i^2=-1$ and $i=\sqrt{-1}$
Thus,
$$=\frac{3-2i+12i-8(-1)}{3^{2}+2^{2}}$$
$$=\frac{11+10i}{13}$$
$$=\frac{11}{13}+\frac{10}{13}i$$
