Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Using the Complex Exponential

  1. Jun 5, 2004 #1


    User Avatar

    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


    User Avatar

    Ahhh, fair enough :)
    Thought it was going to be tedious, but isnt nearly that bad..
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Using the Complex Exponential
  1. Complex Exponential (Replies: 2)

  2. Complex exponential (Replies: 1)

  3. Complex exponentiation (Replies: 6)

  4. Complex exponentiation (Replies: 3)