Imaginary Numbers Question

[O.G]

My friend asked me if he can do this to solve i²

i² = (√ -1)² = √-1 * √ -1 = √ (-1*-1) = 1

(As √ (ab) = √ a * √ b)

The answer is obviously -1, but why can't you do this?

 

[Steven G]

Sqrt(ab)\(\displaystyle \neq\)sqrt(a)*sqrt(b) unless a and b are positive.
'Why can't we do this' has an obvious answer. As YOU see, it does not work if one or both numbers are negative.