>>7318915>Doesn't your "least awful contender" imply, by taking the square root of both sides, that e^i(pi) = 1?
That shit is going on in another thread >>7317019
Basically, when you square a number, the number AND its negative give the same result. So the information is gone whether you started with a negative or positive number.
By the same logic, the inverse of squaring –the square root– should give two results, one positive AND one negative (but we usually discard the negative one). Since you've lost the information of whether it was positive or negative to begin with, you can only reason about the magnitude of the number:
We know that , so any squaring and rooting is invalid if you end up with 1.