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More of a math problem, but from a physics text

  1. Feb 11, 2017 #1
    1. The problem statement, all variables and given/known data Screen Shot 2017-02-11 at 5.38.35 PM.png
    So I can't get from line (53) to line (54)

    I do not understand how interchanging the variables will cause the imaginary part to disappear


    3. The attempt at a solution
    I'm not sure where to start
    I know exp(ix) = cos(x) +isin(x)
    And the only way i see cos(x) coming out is using the exponential identity
    exp(ix) + exp(-ix) = 2cos(x) (but this clearly isn't it)
    But this 'interchanging' variables really doesn't make sense to me
    Please help! The answer is apparently obvious! haha
     
  2. jcsd
  3. Feb 11, 2017 #2

    FactChecker

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    Gold Member

    From the identity e = cos(θ)+i*sin(θ), you can split the real and imaginary parts of the integral. You also know that the cosine is an even function, so cos(-θ) = cos(θ) is used to remove the negative exponent.
    You are over-thinking it. That is not what makes the imaginary part disappear. If you know that the final answer is real, then you know that the imaginary part is zero without having to do anything. So just ignore the sin terms.
     
    Last edited: Feb 11, 2017
  4. Feb 11, 2017 #3
    Oh wow you are right I was overthinking it. Thinking in terms of even and odd functions really helped, thanks!
     
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