real and complex solutions

would the square root of -12 be equal to 12i?

$\begin{array}{|rcll|} \hline && \sqrt{-12} \\ &=& \sqrt{(-1)\cdot 12 } \\ &=& \sqrt{12\cdot (-1) } \\ &=& \sqrt{12}\cdot \sqrt{ -1 } \quad & | \quad \sqrt{ -1 } = i \\ &=& \sqrt{12}\cdot i \\ \hline \end{array}$