What is the shortest way to prove:\[ e^{ix}=\cos(x)+i\sin(x) \]

What is the shortest way to prove:\[ e^{ix}=\cos(x)+i\sin(x) \]

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I know one way is to use the series expansion for cos(x) and sin(x) and show that it matches the series expansion for e^(ix) - but is there a shorter proof?

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

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