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Math Help - Raising complex numbers to a power

  1. #1
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    Hamilton
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    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.
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  2. #2
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    Re: Raising complex numbers to a power

    Quote Originally Posted by biggerleaffan View Post
    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?
    Oh come on, think.

    20\pi\text{rad}~\equiv~ 0\text{rad}
    Thanks from topsquark
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  3. #3
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    Re: Raising complex numbers to a power

    Thank you for your response, Plato.
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