What's your favorite illustration of the usefulness of complex numbers?
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You have the reason on this. But i think that to demosntrate the Euler Identity, you have to know the derivatives of Sen(x) and Cos(x), and in this case it would be a circular reasoning
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No its not correct. You want to prove two formules, based on a formule (Euler identity) that need the formules that you want to prove, to be defined! It not have sense, in this case is a good example of circular reasoning.
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