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Adding two complex functions?

  1. Nov 16, 2008 #1
    How can I show that

    [tex]Aexpi(\omega t - kx + \phi_{1}) + Aexpi(\omega t + kx + \phi_{2}) = 2Aexpi(\omega t + \frac{\phi_{1} + \phi_{2}}{2})cos(kx - \frac{\phi_{1} - \phi_{2}}{2})[/tex]? My book states this without proof, as if it was obvious.
     
  2. jcsd
  3. Nov 16, 2008 #2

    tiny-tim

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    Hi kasse! :smile:

    Hint: eiA + B = eiA + eiB, so divide by the first half of the righthand side, and use eiC + e-iC = 2cosC. :wink:
     
  4. Nov 16, 2008 #3
    Danke schön
     
  5. Nov 16, 2008 #4

    HallsofIvy

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    Oh, dear, oh, dear, oh, dear, tiny-tim! eiA + B = (eiA)(eiB).
     
  6. Nov 16, 2008 #5

    tiny-tim

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    oops!

    Geman for oops! :redface:
     
  7. Nov 16, 2008 #6
    eiA + B = (eiA)(eB)....?
     
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