<s>[INST] Evaluate expression in the form $a+bi$. 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.
 [/INST] Yes it's correct. Just take $a = -6$ and $b = 0$.
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