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Derivative using complex exponential

  1. Apr 10, 2008 #1
    I'm trying find the 15th derivative of exp[(1 + i(3^.5))theta] with respect to theta

    To do this do i need to split it into two exponentials, (e^theta).(e^i(3^.5)theta) ??
     
  2. jcsd
  3. Apr 10, 2008 #2

    HallsofIvy

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    What is the derivative of eax with respect to x? What is its second derivative? What is its 15th derivative? Do you see my point?
     
  4. Apr 10, 2008 #3
    [(1+i(3^.5))^15].e^[(1+i(3^.5))theta]

    So i can just apply the normal rules for exponentials ??
     
  5. Apr 10, 2008 #4

    HallsofIvy

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    Yes, 1+i(3^.5) is "just a number". You might want to use De Moivre's formula to caculate [itex](1+ i\sqrt{3})^{15}[/itex] itself.
     
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