part and parcel of this proof is the fact that the derivative of f(x) = cos(x) + i sin(x) satisfies the differential equation f'(x) = k*f(x) whose solutions are exponential functions
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Agreed, but I was trying to do it with out differential equations even though one could argue that I snuck some diff eq in there
End of conversation
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Write exp(i \theta) = \sum (i^k \theta^k) /k!. Now take real and imaginary part and use the definition of cos and sin.
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