# Problem in complex number multiplication [duplicate]

I want to know $$\sqrt{-m}\sqrt{-n}=$$? I tried in the following ways:

Way 1:$$\sqrt{-m}\sqrt{-n}=\sqrt{(-m)(-n)}=\sqrt{mn}.$$ Way 2:$$\sqrt{-m}\sqrt{-n}=\sqrt{m}i\sqrt{n}i=\sqrt{mn}i^2=-\sqrt{mn}$$

So I got two different values for the same $$\sqrt{-m}\sqrt{-n}$$. How can that be possible?

## marked as duplicate by Saad, Lord Shark the Unknown, Watson, Cesareo, BrahadeeshDec 1 '18 at 10:18

The rule $$\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$$ doesn't necessarily apply when $$a < 0$$ or $$b < 0$$. For example, $$-1 = i\cdot i = \sqrt{-1} \cdot \sqrt{-1} \neq \sqrt{(-1)\cdot(-1)} = \sqrt{1} = 1$$ Therefore, the 1st way is incorrect.