Answer
$$ - \frac{1}{8} + \frac{{\sqrt 3 }}{8}i$$
Work Step by Step
$$\eqalign{
& \frac{{2\left( {\cos {{60}^ \circ } + i\sin {{60}^ \circ }} \right)}}{{8\left( {\cos {{300}^ \circ } + i\sin {{300}^ \circ }} \right)}} \cr
& {\text{Then,}} \cr
& = \frac{{2\operatorname{cis} {{60}^ \circ }}}{{8\operatorname{cis} {{300}^ \circ }}} \cr
& {\text{Simplifying}} \cr
& {\text{ = }}\frac{1}{4}\operatorname{cis} \left( {{{60}^ \circ } - {{300}^ \circ }} \right) \cr
& {\text{ = }}\frac{1}{4}\operatorname{cis} \left( { - {{240}^ \circ }} \right) \cr
& {\text{Write in the rectangular form}} \cr
& {\text{ = }}\frac{1}{4}\left( {\cos {{240}^ \circ } + i\sin \left( { - {{240}^ \circ }} \right)} \right) \cr
& {\text{ = }}\frac{1}{4}\left( { - \frac{1}{2} + i\left( {\frac{{\sqrt 3 }}{2}} \right)} \right) \cr
& = - \frac{1}{8} + \frac{{\sqrt 3 }}{8}i \cr} $$
