Answer
$\frac{2(cos60^\circ + isin60^\circ)}{8(cos300^\circ + isin300^\circ)}$
= $-\frac{1}{8} + \frac{\sqrt{3}}{8}i$
Work Step by Step
$\frac{2(cos60^\circ + isin60^\circ)}{8(cos300^\circ + isin300^\circ)}$
= $\frac{2}{8} [cos(60^\circ - 300^\circ) + isin(60^\circ - 300^\circ)]$ (Quotient Theorem)
= $\frac{1}{4} [cos(-240^\circ) + isin(-240^\circ)]$
= $\frac{1}{4} (-\frac{1}{2} + \frac{\sqrt{3}}{2}i)$
= $-\frac{1}{8} + \frac{\sqrt{3}}{8}i$
