Answer
$\frac{1}{2 - 2i}$
= $\frac{1}{4} + \frac{1}{4} i$
Work Step by Step
Now, 1 is at $0^\circ$ with unit 1, and, $2 - 2i$ is at $315^\circ$ with absolute value $\sqrt{2^2 + (-2)^2} = \sqrt{8}$
Therefore, $\frac{1}{2 - 2i}$
= $\frac{1cis0^\circ}{\sqrt{8}cis315^\circ}$
= $\frac{1}{\sqrt{8}} cis(0^\circ - 315^\circ)$ (Quotient Theorem)
= $\frac{1}{\sqrt{8}} cis(-315^\circ)$
= $\frac{1}{\sqrt{8}} (\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} i)$
= $\frac{1}{4} + \frac{1}{4} i$
