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Homework Help: Complex numbers powers and logs

  1. Sep 28, 2010 #1
    1. The problem statement, all variables and given/known data

    (-e)^iπ answer is -e^-π2

    not sure how to describe this one, but i need to find the roots.

    2. Relevant equations

    (r^n)e^(itheta)n = (r^n)cos(thetan) + isin(thetan) n is an element of the reals

    3. The attempt at a solution


    i'm not sure what to do with this, it is the most weird question on the page. it seems circular to me.
     
  2. jcsd
  3. Sep 28, 2010 #2
    I'm not sure exactly what you are asking here. Here is my attempt at some help.

    When dealing with complex numbers, we can use De Moivre's formula to find roots.

    [tex]\alpha={r}{e}^{i\theta}[/tex]

    [tex]\alpha^{\frac{p}{q}}={r}^{\frac{p}{q}}{exp(ip({\theta}+2n{\pi})/q)}[/tex]

    Example: Find the roots of

    [tex]i^{\frac{1}{3}}[/tex]

    Using:

    [tex]i=e^{\frac{i{\pi}}{2}}[/tex]

    And the above equation gives the roots as:

    [tex]e^{\frac{i{\pi}}{6}}[/tex]

    [tex]e^{\frac{5i{\pi}}{6}}[/tex]

    [tex]e^{\frac{9i{\pi}}{6}}[/tex]

    I hope that helps.
     
  4. Sep 28, 2010 #3
    not really because applying that i still don't get the right answer. I've done many of these types of questions, its just that this one is really weird.

    like if i ln and then put it to the e, it is the same thing...
     
  5. Sep 28, 2010 #4
    You want to find the roots of a function, right? For which function do you want to find the roots?
     
  6. Sep 29, 2010 #5
    -e^ipi i know the answer is -e^(-ipi^2)
     
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