Answer
$$1.9563 + 0.4158i$$
Work Step by Step
$$\eqalign{
& \frac{{45\left( {\cos \frac{{2\pi }}{3} + i\sin \frac{{2\pi }}{3}} \right)}}{{22.5\left( {\cos \frac{{3\pi }}{5} + i\sin \frac{{3\pi }}{5}} \right)}} \cr
& {\text{Use the quotient theorem}} \cr
& = \frac{{45}}{{22.5}}\left[ {\cos \left( {\frac{{2\pi }}{3} - \frac{{3\pi }}{5}} \right) + i\sin \left( {\frac{{2\pi }}{3} - \frac{{3\pi }}{5}} \right)} \right] \cr
& = 2.027\left( {\cos \frac{\pi }{{15}} + i\sin \frac{\pi }{{15}}} \right) \cr
& {\text{Use a calculator }}\left( {{\text{radian mode}}} \right) \cr
& \approx 1.9563 + 0.4158i \cr} $$
