In the context of Quantum mechanics, what is $(-1)^{\left(\frac{-1}{2}\right)}$ really, $i$ or $-i$?
What is wrong with this false proof? $-1=(-1)^1=(-1)^\frac{2}{2}=((-1)^2)^\frac{1}{2}=\sqrt{(-1)^2}=\sqrt{1}=1$