Answer
$$2i$$
Work Step by Step
$$\eqalign{
& \frac{{12\left( {\cos {{23}^ \circ } + i\sin {{23}^ \circ }} \right)}}{{6\left( {\cos {{293}^ \circ } + i\sin {{293}^ \circ }} \right)}} \cr
& {\text{Using the Quotient Theorem}} \cr
& = \frac{{12}}{6}\left[ {\cos \left( {{{23}^ \circ } - {{293}^ \circ }} \right) + i\sin \left( {{{23}^ \circ } - {{293}^ \circ }} \right)} \right] \cr
& {\text{Simplify}} \cr
& = 2\left[ {\cos \left( { - {{270}^ \circ }} \right) + i\sin \left( { - {{270}^ \circ }} \right)} \right] \cr
& = 2\left[ {\cos \left( {{{270}^ \circ }} \right) - i\sin \left( {{{270}^ \circ }} \right)} \right] \cr
& {\text{Write in Rectangular form}} \cr
& = 2\left[ {0 - i\left( { - 1} \right)} \right] \cr
& = 2i \cr} $$
