I didn't know this. The comments are good too, e.g. >>> From the first few seconds of the video, I know where this is going and the answer is: the exponential

I didn't know this. The comments are good too, e.g. >>> From the first few seconds of the video, I know where this is going and the answer is: the exponential function is not injective over C, so you can't cancel it. exp(x) = exp(y) implies x-y is an integer multiple of pi, so not necessarily equal.