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Do you know what is the polar form of a complex number ?

yes

I read once a short proof by using differential equations.

Look here http://en.wikipedia.org/wiki/Euler%27s_formula#Proofs

@FoolForMath - do you mean this:
|dw:1325522941156:dw|

You're welcome!

thanks @FoolForMath

The complex number approach has been explained there too.

i don't think there is a shorter way than series expansion

Using the uniqueness theorem with differentials seems to be the shortest method.

I guess it all depends on how you define "shortest"

I still find the proof using derivatives much simpler.

Yes, I agree with you asnaseer.

it look more "elegant" as well.

*looks

yea but inaccessible without knowledge of calculus.

btw asnaseer, what's your need?