Complement of $a^n b^n c^n$
The complement is the set of all strings over alphabet $\{a,b,c\}$ that are not of the form $a^i b^i c^i$ for some $i\geq 0$.  That includes all strings $a^ib^jc^k$ where $i\neq j$, $i\neq k$ and/or $j\neq k$, as you say, but also some other strings.  Mouse-over the box below for a hint.


   For example, $bacbabc$ is in the complement.