Answer
$2+3i$ ohms
Work Step by Step
We are given the voltage: $V=18+i$ and current $I=3-4i$. We find the impedance, Z:
$\displaystyle Z=\displaystyle \frac{V}{I}$
$\displaystyle =\frac{18+i}{3-4i}$
$\displaystyle =\frac{18+i}{3-4i}*\frac{3+4i}{3+4i}$
$\displaystyle =\frac{54+72i+3i+4i^{2}}{9+12i-12i-16i^{2}}$
$\displaystyle =\frac{54+75i+4*-1}{9+16}$
$\displaystyle =\frac{50+75i}{25}$
$\displaystyle =2+3i$ ohms
