# Raising complex numbers to a power

• Jun 5th 2013, 03:08 PM
biggerleaffan
Raising complex numbers to a power
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.
• Jun 5th 2013, 03:17 PM
Plato
Re: Raising complex numbers to a power
Quote:

Originally Posted by biggerleaffan
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?

Do not ever double post!

You can be banned for doing that,