Complex number qs (1 Viewer)

[Joshmosh2]

http://m.imgur.com/SeuqmHu

Idk what to do for the first one
For the second, I used sum of gp, but couldn't get the answer.

Answers are 16root2(cos^4(pi/16)) and (1+root2)i respectively

*edit - for the second q, mistakenly took n to be 20 instead of 21.

 

[HeroicPandas]

Q1) Apply double-angle formulas for cosine and sine

Q2) Notice that the sum is a geometric progression..?