Answer
$$ - 6 + 6\sqrt 3 i$$
Work Step by Step
$$\eqalign{
& \frac{{24\left( {\cos {{150}^ \circ } + i\sin {{150}^ \circ }} \right)}}{{2\left( {\cos {{30}^ \circ } + i\sin {{30}^ \circ }} \right)}} \cr
& {\text{Using the Quotient Theorem}} \cr
& = \frac{{24}}{2}\left[ {\cos \left( {{{150}^ \circ } - {{30}^ \circ }} \right) + i\sin \left( {{{150}^ \circ } - {{30}^ \circ }} \right)} \right] \cr
& {\text{Simplify}} \cr
& = 12\left[ {\cos \left( {{{120}^ \circ }} \right) + i\sin \left( {{{120}^ \circ }} \right)} \right] \cr
& {\text{Write in Rectangular form}} \cr
& = 12\left( { - \frac{1}{2} + \frac{{\sqrt 3 }}{2}i} \right) \cr
& = - 6 + 6\sqrt 3 i \cr} $$
