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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.

The mistake is presenting it as a video.

There must be a worse way of presenting a proof. Interpretive dance? A series of perfumes? But YouTube is certainly high on the list.