How to take complement of a language?
You are right. The complement consists of all strings not in the language. So basically if the language says "all strings such that X holds" the complement is "all strings such that not X holds", the logical negation of X.

In this case the logical negation of "$i=j$ and $i=k$" equals "not ($i=j$ and $i=k$)" or using the Morgan's rule, "$i\neq j$ or $i\neq k$".

But there is a slight catch. Actually the strings in $L$ have an additional explicit condition, they are of the form $a^i b^j c^k$ for some $i,j,k$. That means the actual complement is the union of (1) all strings not of the form $a^i b^j c^k$ (thus, not in $a^* b^* c^* $) and (2) all strings of the form $a^i b^j c^k$ such that "$i\neq j$ or $i\neq k$".

The strings in (1) form the regular language $\{a,b,c\}^* - a^* b^* c^* $ and should not bother you too much. The strings in (2) are treated elsewhere in this forum.