if sqrt(2)*sqrt(8) = sqrt(2*8) why isnt sqrt(-1)*sqrt(-1)=sqrt(-1*-1)
\(if\;\; \sqrt2*\sqrt8= \sqrt{2*8}\\\text{ why isn't }\quad\\ \sqrt{-1}*\sqrt{-1}=\sqrt{-1*-1}\)
The rules for real numbers often do not extend to imaginary numbers.
This is one such case.
Alan, or someone else might be able to give a better explanation. :/