By definition, $i^2=-1$, right?
But one can then clearly deduce that $(-i)^2=-1$. The only difference I see is that one is $-1$ times the second.
So what allows us to differentiate between $i$ and $-i$? Can they be used synonymous? That is, does nothing happen if all of a sudden we were to switch $i$ and $-i$ in math, so long as we are consistent?
There is some interesting mathematics bound up in your question. There is an automorphism of $\mathbb C$ as a field extension of $\mathbb R$ which is defined by sending $i$ to $-i$. Provided you are consistent (including very great care with signs) everything algebraic works nicely. This reflects the fact that in building $\mathbb C$ from $\mathbb R$ we make an arbitrary choice of a square root of $-1$ to call $i$.
For amusement there is an automorphism of $\mathbb Q(\sqrt 2)$ as an extension of $\mathbb Q$ which sends $\sqrt 2$ to $-\sqrt 2$ - for much the same reason. However, interesting things happen to the metric (distance between points) - so though the algebraic properties are retained, it is not true that "everything" remains the same.