Evaluate expression in the form $a+bi$.

Question

So, I have to evaluate $\sqrt{-3}\sqrt{-12}$ into the form $a+bi$.
I know that $i^2 = -1$ so $i = \sqrt{-1}$
What I have done is:

$$\begin{align}\sqrt{-3}\sqrt{-12} &= \sqrt{3(-1)}\sqrt{12(-1)}\\ &= \sqrt{3}i\sqrt{12}i\\ &= \sqrt{3}\cdot i\cdot 2\sqrt{3}\cdot i\\ &= 3\cdot 2\cdot (i^2)\\ &= 6\,i^2\\ &= 6\cdot (-1)\\ &=-6\end{align}$$

So, my question is if I have to have the expression in the form $a+bi$ is my answer of $-6$ still correct? Thanks.

Answer 1

Yes it's correct. Just take $a = -6$ and $b = 0$.

Answer 2

Yes, because $$-6 = -6 + 0i.$$ If in doubt, you may want to write it down.