TITLE: How do i show this :$\sum_{k=0}^{n}\cos kx+i\sum_{k=0}^{n}\sin kx $ is a geometric sequence with complex ratio?
QUESTION [0 upvotes]: I have tried to show that this:$$\sum_{k=0}^{n}\cos kx+i\sum_{k=0}^{n}\sin kx $$ is a geometric sequence  with complex ratio but i don't succed , I have use transformation with Euler identity of cos and sin but no result , any help ?   
Note: $i$ is unitary imaginary part

REPLY [3 votes]: Hint:
Think of De Moivre's formula
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