<s>[INST] 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.
 [/INST] $$\frac{\cos\frac{20\pi}{3}+i\sin\frac{20\pi}{3}}{\cos{\frac{15\pi}{4}}{+i\sin\frac{15 \pi}{4}}}=\frac{e^{i\frac{20\pi}{3}}}{e^{i\frac{15\pi}{4}}}$$
$$=e^{i\frac{20\pi}{3}-i\frac{15\pi}{4}}$$
$$=e^{i\frac{35}{12}}$$
$$=\cos\frac{35\pi}{12}+i\sin\frac{35 \pi }{12}$$
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