## Trigonometry (11th Edition) Clone

$\frac{1}{2 - 2i}$ = $\frac{1}{4} + \frac{1}{4} i$
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) = $\frac{1}{\sqrt{8}} cis(-315^\circ)$ = $\frac{1}{\sqrt{8}} (\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} i)$ = $\frac{1}{4} + \frac{1}{4} i$