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I’m sorry to contradict your extremely cool comment, but I’m pretty sure that e^(-i*π) = -1 (and in fact so is e^(i*π) ).  ( e^(-i*2π) and e^(i*2π) are indeed 1, but that isn’t nearly as cool).
I’m sorry to contradict your extremely cool comment, but I’m pretty sure that e^(-i*π) = -1 (and in fact so is e^(i*π) ).  ( e^(-i*2π) and e^(i*2π) are indeed 1, but that isn’t nearly as cool).