why is e^(iπ)+1=0?

Question

why is e^(iπ)+1=0?

anonymous · Answer

Thank you guys~

myininaya · Answer

$$e^{i \pi} =\cos(\pi)+i \sin(\pi)=-1+i (0)=-1+0=-1$$

myininaya · Answer

$$-1+1=0$$

anonymous · Answer

e iπ =cos(π)+isin(π) but why?Satisfy my curiosity~

anonymous · Answer

http://en.wikipedia.org/wiki/Euler%27s_formula

anonymous · Answer

I can't visit the wikipedia I'm in China

anonymous · Answer

use proxy

anonymous · Answer

I tried but the network in my house in veeeery slow

anonymous · Answer

$$e ^{i  x}=cosx+isinx$$

turingtest · Answer

that's the short answer above
you can prove that$$e^{ix}=\cos x+i\sin x$$by using$$e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+...$$$$\sin x=x-\frac{x^3}{3!}+\frac{x^5}{5!}-...$$$$\cos x=1-\frac{x^2}{2!}+\frac{x^4}{4!}-...$$
try plugging in $$e^{ix}$$into that expansion for e^x and you will see that it will amount to $$\cos x+i\sin x$$

anonymous · Answer

Wikepedia is banned in china? !!!

turingtest · Answer

everything is banned in China

anonymous · Answer

is wikileaks banned in US?

anonymous · Answer

no it's not

anonymous · Answer

Is any news network other than Fox banned in the US? :-P

anonymous · Answer

haha :D

anonymous · Answer

Look at that ----so many people Hi!~

anonymous · Answer

That awkward moment when you say "Hi!" and not a single other comment is made... :-P
Sup chum.

turingtest · Answer

it's a cool question, people like to answer it.

anonymous · Answer

Or just read the cool answers provided.

anonymous · Answer

Thanks again

anonymous · Answer

here is the wikipedia article in pdf

anonymous · Answer

you won't believe that the net-speed in my house is less than1M 200kb/s