Answer
$-\frac{5}{17}+\frac{14}{17}i$
Work Step by Step
Given: $\displaystyle \frac{3+2i}{1-4i}$
Multiply the numerator and denominator by the conjugate of the denominator:
$=\frac{3+2i}{1-4i}\times\frac{1+4i}{1+4i}$
Since, $i^2=-1$ and $i=\sqrt{-1}$
Thus,
$=\frac{3+12i+2i+8(-1)}{1^{2}+4^{2}}$
$=\frac{-5+14i}{17}$
$=-\frac{5}{17}+\frac{14}{17}i$
