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.

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!

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Re: Raising complex numbers to a power

Sorry Plato, did not read the rules