The set of all complex numbers $a+bi$ is denoted by $\mathbb{C}$ (or sometimes just by $\textbf{C}$). Your problem is referring to $\mathbb{C}^3$, which is the set of vectors $(z_1,z_2,z_3)$ where $z_1$, $z_2$, and $z_3$ are complex numbers.
Many things work analogously when you deal with complex vectors vs. regular vectors. If you take the cross product of two vectors in $\mathbb{R}^3$, you get back a new vector orthogonal to both of the original vectors. The same works for complex numbers, and you can check this yourself. (What tests of orthogonality do you know?)
Finally, it is important to realize that there is not just one answer to this question. In fact, there are infinitely many answers. If $v$ is in $\mathbb{C}^3$, and is perpendicular to both $A$ and $B$, then so will be $2v$, $(1+3i)v$, or any complex multiple of $v$. Hopefully you will understand this phenomenon better as you go on with your linear algebra class!