Question

explain how e^(ix) = cosx + i*sin(x) please

Answer 1

http://en.wikipedia.org/wiki/Euler's_formula#Proofs

Answer 2

you can see it if you take the power series for for exp(x), then replace x by ix to get the power series for exp(ix)

then take the power series for cosine, the power series for sine, multiply it by i, add them together, and see that you get the same thing.

Answer 3

Yes, that is a proof. The limiting process in the complex plane is more of an explanation of how they are connected.