Set notation of the set of all strings How do I present the complement using set notation?

I guess it has to be shows with universal set - {aa,bb} but I do not know how to represent the universal set in terms of set notation. Since, the strings of the universal set can be anything over alphabets {a,b}. So, how to represent it?
I guess something like this might work if we are going from outside to inside {{{a,b}*}*}.
Any help is appreciated.
The universe here is the set of all strings over the alphabet $\{a,b\}$ and is usually denoted by $\{a,b\}^*$.

You have way too many brackets.