Not sure where to put this ... I saw this some time ago, but could never really figure out what/where the problem is:

$\displaystyle i=\sqrt{-1}$

$\displaystyle i^2=(\sqrt{-1})^2=-1$

$\displaystyle \sqrt{-1} \cdot \sqrt{-1}=-1$

$\displaystyle \sqrt{(-1) \cdot (-1)}=-1$

$\displaystyle \sqrt{1}=-1$

$\displaystyle 1=-1$

As far as I can tell, the process seems to be valid, but obviously 1 is not -1 ... so what exactly is wrong?