Answer
$\displaystyle-\frac{1}{2}+\frac{5}{2}i$
Work Step by Step
Recall, $i=\sqrt{-1}$, so $i^{2}=-1$. Thus, we multiply by the conjugate of the denominator to obtain:
$\displaystyle \frac{2+3i}{1-i}$
$\displaystyle=\frac{2+3i}{1-i}*\frac{1+i}{1+i}$
$\displaystyle=\frac{2+2i+3i+3i^{2}}{1+i-i-i^{2}}$
$\displaystyle=\frac{2+5i+3*-1}{1--1}$
$\displaystyle=\frac{-1+5i}{2}$
$\displaystyle=-\frac{1}{2}+\frac{5}{2}i$
