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## Main Question or Discussion Point

Hi

I was trying to prove Euler's formula in complex numbers that states : [PLAIN]http://upload.wikimedia.org/math/d/c/4/dc4d000103c1293c5cde00fac04850d6.png. [Broken] I tried to prove it by taylor series but the problem is that I don't know if my proof is right or not. I think taylor series work only when x approaches to some number a, so it doesn't apply to all values of f(x). thus when I write 1 + ix + (ix)2/2! + ... it means that i'm proving the formula only when approaches zero. can anyone help me and correct me if i'm wrong or approve me if i'm right? and does anyone know an accurate proof of the formula?

thanks

I was trying to prove Euler's formula in complex numbers that states : [PLAIN]http://upload.wikimedia.org/math/d/c/4/dc4d000103c1293c5cde00fac04850d6.png. [Broken] I tried to prove it by taylor series but the problem is that I don't know if my proof is right or not. I think taylor series work only when x approaches to some number a, so it doesn't apply to all values of f(x). thus when I write 1 + ix + (ix)2/2! + ... it means that i'm proving the formula only when approaches zero. can anyone help me and correct me if i'm wrong or approve me if i'm right? and does anyone know an accurate proof of the formula?

thanks

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