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Math Help - Complex number and exponents

  1. #1
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    Complex number and exponents

    Hello everyone,

    I need to perform the following operation: (1+2i)^214. Can I just follow the same guideline as if I didn't have a real part, ie (1+2i)^((53x4)+2) = (1+2i)^2 = -3+4i, or does this little trick only apply when the exponent is attached only to the imaginary part?

    If I cannot perform the operation this way, how should I proceed about it?

    Many thanks!

    Egoyan
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  2. #2
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    Re: Complex number and exponents

    You have to start by expressing the number in exponential or polar form.
    Last edited by BobP; February 23rd 2013 at 06:55 AM.
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  3. #3
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    Re: Complex number and exponents

    Quote Originally Posted by Egoyan View Post
    I need to perform the following operation: (1+2i)^214.
    If I cannot perform the operation this way, how should I proceed about it?
    If you are not working on an actual application, then this is a pointless problem.

    Let \theta=\arctan\left(2\right) then 1+2i=\sqrt{5}\exp(i\theta).

    Thus (1+2i)^{214}=5^{107}\exp(214i\theta)

    Of course that can be reduced: \mod(214\cdot\theta,2\pi)\sim 4.451969
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  4. #4
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    Re: Complex number and exponents

    It's just a question there is in a math homework I have.

    Right, I should have thought about that. I expressed the number in polar form and it was indeed pretty easy from there. Thanks guys.
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