The ambiguity comes from the definition of i and -i from algebraic perspective. They are two roots of sqrt(-1) and they have indistinguishable properties other

The ambiguity comes from the definition of i and -i from algebraic perspective. They are two roots of sqrt(-1) and they have indistinguishable properties other than the fact that they are different. I.e. if we live in an alternate world where the complex plane is flipped (j = -i) then there is no way to distinguish this world between the original. It’s similar to the inherent ambiguity between left and right - the only defining characteristics of them are they are opposite to each other. Note that 1 and -1 have different mathematical properties (in most cases - in Z/2 they would be equal) that allow us to distinguish. 1 * x = x but -1 * x = -x.