What's your favorite illustration of the usefulness of complex numbers?
This is actually proving the derivatives of trig functions tho
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To be fair, it looks like the actual proof of those would be seen in the first equality of the second line of math. It's a good trick to remember the derivatives, but not really a proof of their values.
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this constitutes a proof under the assumptions (e^(ax))' = a*e^(ax) and e^(ix) = cos(x) + i*sin(x)
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it's a beautiful proof, don't get me wrong!
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