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Confusing Step - Euler's Formula?

  1. Nov 9, 2009 #1
    I'm following the answer to a problem and I see this step which I am unsure about:


    [tex]F[k]=\frac{1}{2}\int^{1}_{-1}|x|e^{-\pi i k x}dx[/tex]

    [tex]F[k]=\frac{1}{2}\int^{1}_{-1}|x|cos(\pi k x)dx[/tex]

    For k equal to all integers.


    Shouldn't the conversion from the exponential be [tex]cos(-\pi k x)[/tex]
     
  2. jcsd
  3. Nov 9, 2009 #2
    Crap, wrong section
     
  4. Nov 9, 2009 #3

    Mark44

    Staff: Mentor

    [tex]e^{-i \pi k x}~=~cos(- \pi k x) + i sin(- \pi k x)[/tex]

    cos(-u) = cos(u)
     
  5. Nov 9, 2009 #4
    ...Duh...

    Thanks.
     
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