Multiplication of two imaginary numbers. While reading about the complex numbers I found a property $\sqrt{-a} = i \sqrt{a}$. Further it was stated that
$\sqrt{-a}×\sqrt{-b}=i \sqrt{a}×i \sqrt{b}= -\sqrt{ab}$.
Suppose I take two numbers $\sqrt{-3}$ and $\sqrt{-2}$ and if I multiply both, then according to above statement $\sqrt{-3}×\sqrt{-2}= -\sqrt{3×2}= -\sqrt{6}= -2.449$.This gives a negative real number. But when I multiplied it in calculator then it gave me MATH ERROR. Why?
Also it was given that doing $\sqrt{-a}×\sqrt{-b} = \sqrt{(-a)×(-b)}$ is wrong as it further becomes $\sqrt{ab}$ but answer is $-\sqrt{ab}$. This also means I cannot separate $\sqrt{(-a)×(-b)}$ to $\sqrt{-a}×\sqrt{-b}$. But for $\sqrt{-a} = i \sqrt{a}$, we have separated $\sqrt{(-1×a)}$ to $\sqrt{-1}×\sqrt{a}$ which we further write as $i \sqrt{a}$. Why?

Your answer is right. calculator you used does not support complex arithmetic.
see this calculation in wolframalpha
