Answer
$-\frac{5}{17}+\frac{14}{17}i$
Work Step by Step
$\displaystyle \frac{3+2i}{1-4i}$
We multiply the numerator and denominator by the conjugate of the denominator:
$=\frac{3+2i}{1-4i}\cdot\frac{1+4i}{1+4i}$
We use the fact that $i^2=-1$ (because $i=\sqrt{-1}$)
$=\frac{3+12i+2i+8*-1}{1^{2}+4^{2}}$
$=\frac{-5+14i}{17}$
$=-\frac{5}{17}+\frac{14}{17}i$
