Solve this other than punching out actual numbers

  • Thread starter kreil
  • Start date
  • #1
kreil
Insights Author
Gold Member
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?
 

Answers and Replies

  • #2
CTS
20
0
e^ix = cos x + i sin x
 
  • #3
kreil
Insights Author
Gold Member
668
68
thanks, I didn't know about that equation
 
  • #4
mathman
Science Advisor
7,942
496
If you look at the power series for cos(x), sin(x) and eix, the relationship will be obvious.
 

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