What's your favorite illustration of the usefulness of complex numbers?
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How do you define Exp(ix)?
the unique function that satisfies the differential equation df/dx = f with initial condition f(0)=1
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that's the definiton of e^z
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Well, that's A definition, and a perfectly viable one. How do YOU prove Euler's formula from this definition? I've found people usually prove it with the power series definitions. Again, I think something is being swept under the rug, I just don't know where yet.
End of conversation
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