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Solve this other than punching out actual numbers 
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#1
Nov2104, 08:15 AM

P: 538

[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
Nov2104, 10:59 AM

P: 20

e^ix = cos x + i sin x



#4
Nov2104, 03:50 PM

Sci Advisor
P: 6,040

Solve this other than punching out actual numbers
If you look at the power series for cos(x), sin(x) and e^{ix}, the relationship will be obvious.



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