Answer
$\frac{45(cos(\frac{2\pi}{3}) + isin(\frac{2\pi}{3}))}{22.5(cos(\frac{3\pi}{5}) + isin(\frac{3\pi}{5}))}$
= $1.9563 + 0.4158i$
Work Step by Step
$\frac{45(cos(\frac{2\pi}{3}) + isin(\frac{2\pi}{3}))}{22.5(cos(\frac{3\pi}{5}) + isin(\frac{3\pi}{5}))}$
= $2 cis(\frac{2\pi}{3} - \frac{3\pi}{5})$ (Quotient Theorem)
= $2 cis(\frac{\pi}{15})$
= $1.9563 + 0.4158i$ (Using calculator and corr. to 4 decimal places)