Closure properties of non-context-free languages (concatenation & complement)
As for closure under complementation -- consider the following hint: context-free languages are not closed under complementation.

Regarding concatenation, this is slightly more tricky, but non-context free languages are not closed under complementation. 

There are many ways of finding counterexamples for the latter, one is the following "trick":

Let $L$ be some non-context free language over some alphabet $\Sigma$, that does not contain $0,1$. Now define two languages: $A=(1\cdot \Sigma^*)\cup (0\cdot L)\cup \{\epsilon\}$ and 
$B=(0\cdot \Sigma^*)\cup (1\cdot L)\cup \{\epsilon\}$

It is not hard to prove that neither $A$ nor $B$ are context free, basically due to presence of $L$.

However, we have that $A\cdot B=\{0,1\}\cdot \Sigma^*\cup \{\epsilon\}$, which is regular (and in particular context-free).