Answer
$\frac{w}{z}$
= $-i$
Work Step by Step
For $w = -1 + i$ and $z = -1 -i$, the quotient $\frac{w}{z}$ is
$\frac{w}{z}$
= $\frac{-1 + i}{-1 - i}$
= $\frac{-1 + i}{-1 - i}\cdot \frac{-1 + i}{-1 + i}$
= $\frac{(-1+i)^2}{2}$
= $\frac{(-1)^2+2(-1)i+i^2}{2}$
= $\frac{1-2i-1}{2}$ ($i^2 = -1$)
= $-i$