Question :
Explain this fallacy:
$$-1=\sqrt{-1}\sqrt{-1}=\sqrt{(-1)(-1)}=\sqrt{1}=1$$
(Complex Variables Schaum c1:1.128)
Btw, it's not a homework, i'm curious why it can be false?
Well, i'm considering we're not allowed to multiply these two negative numbers under the roots.
But, what is the reason? Could it be proven? Or it's just an agreement?
$\sqrt{(-1)(-1)}$ is not equal to $\sqrt{-1}\cdot\sqrt{-1}$.