Answer
$\frac{w}{z}$
= $cos(-90^\circ) + isin(-90^\circ)$ or $-i$
Work Step by Step
For $w = -1 + i$ or $\sqrt{2}cis135^\circ$ in trigonometric form and
$z = -1 -i$ or $\sqrt{2}cis225^\circ$ in trigonometric form,
the quotient $\frac{w}{z}$ is
$\frac{w}{z}$
= $\frac{\sqrt{2}cis135^\circ}{\sqrt{2}cis225^\circ}$
= $\frac{\sqrt{2}}{\sqrt{2}} cis(135^\circ - 225^\circ)$ (Quotient Theorem)
= $cis(-90^\circ)$
= $cos(-90^\circ) + isin(-90^\circ)$
= $-i$
