complex numbers - What is wrong with my proof: $-1 = 1$?

I have some theories about why this could by wrong but I still haven't something that convinces me. What is wrong with this proof:

$-1 = i^2 = i.i = \sqrt{-1}.\sqrt{-1} = \sqrt{(-1).(-1)}= \sqrt1 = 1$

This would imply that:
$1 = -1$

Which is obviously false.

So my theory is that it's not a great idea to write $i = \sqrt{-1}$, but I'm not sure why...

Answer

The flaw is in assuming that the rule $\sqrt x\sqrt y=\sqrt{xy}$ holds with imaginary numbers. You just show us a counter-example.