Which is right (and why)?

$\displaystyle 17I+4-2 \cdot \sqrt{-2} \cdot \sqrt{-18} = 17I+4-2I \cdot \sqrt{2} \cdot I\sqrt{18}= \ldots = 16+17I$

or

$\displaystyle 17I+4-2 \cdot \sqrt{-2} \cdot \sqrt{-18} = 17*I+4-2 \cdot \sqrt{36}= \ldots = -8+17I$

Actually, according to my calculator, the first one is right, so I really only want to know why.

Isn't $\displaystyle \sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$? If so, then $\displaystyle \sqrt{-2} \cdot \sqrt{-18} = \sqrt{(-2)(-18)} = \sqrt{36}=6$ and the second one is "also" right.

Note that my calc says:

$\displaystyle \sqrt{(-2)(-18)}=6$, and

$\displaystyle \sqrt{-2} \cdot \sqrt{-18}=-6$

Is the conclusion that $\displaystyle \sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$ is only true for $\displaystyle a,b \ge 0$?

Thanks