Hi there,

I have something such as:

(1/2 + i[sqrt3]/2)^60

I know using De Moivre's theorem I have:

z^n = r^n (cos(ntheta) + isin(ntheta)

with n=the power and r=modulus of the complex number

And with r=1 I get

1(cos(20pi) + isin(20pi))

And using Euler's theorem I get:

e^i20pi = 1

However, I am confused on why e^i20pi = 1 (I know this is the answer because of the solutions provided). Could anyone help explain this to me? Or help with an easier way of achieving the answer 1?

Thank you.