Solve this other than punching out actual numbers

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

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

    e^z = 1 + z + \frac{z^2}{2!} + \frac{z^3}{3!}+...+\frac{z^n}{n!}



    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. e^ix = cos x + i sin x
  4. thanks, I didn't know about that equation
  5. mathman

    mathman 6,618
    Science Advisor
    Gold Member

    If you look at the power series for cos(x), sin(x) and eix, the relationship will be obvious.
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