Finding Re (α + α^2 + α^3 + α^4 + α^5)

[NEILS BOHR]

Homework Statement

Let alpha = e ^ i8pi / 11 , then find Re ( alpha + alpha ^2 + alpha ^3 + alpha ^4 + alpha ^5).

Homework Equations

The Attempt at a Solution

look i have reduced the expression to $$\alpha$$ ($$\alpha^5$$ -1 ) / $$\alpha$$-1

now what to do??

 

[Ted Sand]

Have you tried using Euler's formula:
e^ix = cosx + isinx