Q:

A quotient of trigonometric expressions in complex analysis

How is $$\frac{\cos\frac{20\pi}{3}+i\sin\frac{20\pi}{3}}{\cos{\frac{15\pi}{4}}{+i\sin\frac{15 \pi}{4}}}=\cos\frac{35\pi}{12}+i\sin\frac{35 \pi }{12}\ \ \ ?$$ 
I think that I am having trouble understanding a fundamental concept in complex analysis, but cannot pinpoint which.

A:

$$\frac{\cos\frac{20\pi}{3}+i\sin\frac{20\pi}{3}}{\cos{\frac{15\pi}{4}}{+i\sin\frac{15 \pi}{4}}}=\frac{e^{i\frac{20\pi}{3}}}{e^{i\frac{15\pi}{4}}}$$
$$=e^{i\frac{20\pi}{3}-i\frac{15\pi}{4}}$$
$$=e^{i\frac{35}{12}}$$
$$=\cos\frac{35\pi}{12}+i\sin\frac{35 \pi }{12}$$

