Answer
$$\sqrt 3 + i$$
Work Step by Step
$$\eqalign{
& \frac{{4\left( {\cos {{150}^ \circ } + i\sin {{150}^ \circ }} \right)}}{{2\left( {\cos {{120}^ \circ } + i\sin {{120}^ \circ }} \right)}} \cr
& {\text{Using the Quotient Theorem}} \cr
& = \frac{4}{2}\left[ {\cos \left( {{{150}^ \circ } - {{120}^ \circ }} \right) + i\sin \left( {{{150}^ \circ } - {{120}^ \circ }} \right)} \right] \cr
& {\text{Simplify}} \cr
& = 2\left[ {\cos \left( {{{30}^ \circ }} \right) + i\sin \left( {{{30}^ \circ }} \right)} \right] \cr
& {\text{Write in Rectangular form}} \cr
& = 2\left( {\frac{{\sqrt 3 }}{2} + i\left( {\frac{1}{2}} \right)} \right) \cr
& = \sqrt 3 + i \cr} $$
