〈 Berger | Dillon 〉

What's your favorite illustration of the usefulness of complex numbers?

This is actually proving the derivatives of trig functions tho

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.

this constitutes a proof under the assumptions (e^(ax))' = a*e^(ax) and e^(ix) = cos(x) + i*sin(x)

Right, but prove that first equation (over complex numbers), and you'll likely see the derivatives pop out in the process. Depending on the method of proof, of course. I couldn't see the earlier slides from your talk.

it follows straight from the limit definition