The square root of any number x is ±y, where +y = (+1)*y = y, and -y = (-1)*y.

So we define i as conforming to ±i = sqrt(-1). The element i itself has no need for a sign, so no sign needs to be chosen. Yet having defined i, we know that that i = (+1)*i = +i, by multiplicative identity.

We now have an unsigned base element for complex numbers i, derived uniquely from the expansion of <R,0,1,+,*> into its own natural closure.

We don't have to ask if i = +i, because it does by definition of the multiplicative identity.

TLDR: Any square root of -1 reduced to a single value, involves a choice, but the definition of unsigned i does not require a choice. It is a unique, unsigned element. And as a result, there is only a unique automorphism, the identity automorphism.