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Using the Complex Exponential

  1. Jun 5, 2004 #1


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    How would one use the complex exponential to find something like this:
    \frac{{d^{10} }}{{dx^{10} }}e^x \cos (x\sqrt 3 )[/tex]
    I'm guessing we'd have to convert the cos into terms of [tex]e^{i\theta }[/tex] but the only thing I can think of doing then is going through each of the derivatives. Im guessing there is another way?

    thanks in advance.
  2. jcsd
  3. Jun 5, 2004 #2
    [tex]e^{i \theta} = \cos{\theta} + i\sin{\theta}[/tex]


    [tex]\cos{\theta} = \frac{e^{i \theta} + e^{-i \theta}}{2}[/tex]

    Then each successive derivative just adds a power to the coefficient of e.

    Last edited: Jun 5, 2004
  4. Jun 5, 2004 #3


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    Ahhh, fair enough :)
    Thought it was going to be tedious, but isnt nearly that bad..
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