Here is the simplest proof I ever saw, done by working backward. Enlarge so you can see the whiteboard. His teaching style encourages class participation. Sine functions are trig, which follows geometry, and a complex number is expressed in standard form when written a + bi where a is the real part and bi is the imaginary part. For example, 5+2i is a complex number. No need to think about that. Watch the teacher. (BTW, Fourier, 1768-1830, was orphaned at age nine. Ergo, I have no excuses when doing math. https://en.wikipedia.org/wiki/Joseph_Fourier)
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