properties of complex number multiplication

Could you please explain to me why this simple equation is true

$$-i * i = 1$$

or

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

I know basic properties of roots

$$\sqrt{a} * \sqrt{b} = \sqrt{a*b}$$

but what I get is

$$-\sqrt{-1} * \sqrt{-1} = -\sqrt{(-1)*(-1)}= -\sqrt{1} = -1$$

Answer

The equality $-i\cdot i=1$ is equivalent to $i\cdot i=-1$.

But $i^2=-1$ is a property of $i$, so you're done.

$\sqrt{-1}$ is not one number, but two numbers:
$\sqrt{-1}=a\iff a^2=-1$, there are two such $a$: $a=i$ and $a=-i$.