- #1
- 668
- 68
[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?
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?