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

Solve this other than punching out actual numbers

  1. Nov 21, 2004 #1

    kreil

    User Avatar
    Insights Author
    Gold Member

    [tex] e^{i\pi}=-1 [/tex]

    I was wondering how on earth this was possible. I know that:

    [tex]
    e^z = 1 + z + \frac{z^2}{2!} + \frac{z^3}{3!}+...+\frac{z^n}{n!}
    [/tex]

    So

    [tex]
    e^{i\pi}=1+i\pi+\frac{-\pi^2}{2!}+\frac{-\pi^3i}{3!}+\frac{\pi^4}{4!}...
    [/tex]

    I was wondering if there is any way to solve this other than punching out actual numbers and seeing about where they converge to?
     
  2. jcsd
  3. Nov 21, 2004 #2

    CTS

    User Avatar

    e^ix = cos x + i sin x
     
  4. Nov 21, 2004 #3

    kreil

    User Avatar
    Insights Author
    Gold Member

    thanks, I didn't know about that equation
     
  5. Nov 21, 2004 #4

    mathman

    User Avatar
    Science Advisor
    Gold Member

    If you look at the power series for cos(x), sin(x) and eix, the relationship will be obvious.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Solve this other than punching out actual numbers
Loading...