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Math Help - Integrating complex exponential function

  1. #1
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    Integrating complex exponential function

    Hello,

    How do I integrate the following:

    \int_{0}^{1} e^{-2\pi x \gamma i}dx

    Thanks.
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by surjective View Post
    Hello,

    How do I integrate the following:

    \int_{0}^{1} e^{-2\pi x \gamma i}dx

    Thanks.
    You can integrate complex valued functions just like real valued functions.

    So  \int e^{-2\pi x \gamma i}dx = \frac{i}{2\pi\gamma}e^{-2\pi x \gamma i} + C

    Can you take it from here?
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  3. #3
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    integrating complex exponential function

    Hey,

    Thanks for the reply.

    How did you arrive at that? Could you please break it down. I have never integrated complex functions before.

    Thanks a million
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  4. #4
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by surjective View Post
    Hey,

    Thanks for the reply.

    How did you arrive at that? Could you please break it down. I have never integrated complex functions before.

    Thanks a million
    Like I said, it's ok to apply the same methods of integration to complex valued functions as real valued functions.

    With that said, what's  \int e^{ax}dx ?
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