Answer
$\frac{w}{z}$
= $2\sqrt{3} + 2i$
Work Step by Step
$w = 12(cos80^\circ + isin80^\circ) = 12cis80^\circ$
$z = 3(cos50^\circ + isin50^\circ) = 3cis50^\circ$
Now, $\frac{w}{z}$
= $\frac{12cis80^\circ}{ 3cis50^\circ}$
= $\frac{12}{3} \cdot cis(80^\circ - 50^\circ)$ (Quotient Theorem)
= $4cis30^\circ$
= $4(cos30^\circ + isin30^\circ)$
= $4(\frac{\sqrt{3}}{2} + \frac{1}{2} i)$
= $2\sqrt{3} + 2i$
