## Why doesn’t Mathematica ComplexExpand integrals?

Consider this code example:

``ComplexExpand[Re[Integrate[f[t], {t, a, b}]]] ``

Mathematica gives me the result as

``Re[Integrate[f[t], {t, a, b}]] ``

which is obviously not helpful and not what should happen in my understanding. If all variables are real – and that’s what `ComplexExpand` assumes according to the documentation – then `Re` can be dropped from the expression. The same happens for `Im`. This seems to confuse `FullSimplify` which leaves me with a long expression that could be shorted. Why is this the case?

## Simplifying complex expresion (without ComplexExpand or User defined rules)

Many times, I’ve struggled with simplifying complex expressions, such as this extraordinarily simple expression, and Mathematica wont do it:

``\$  Assumptions = {l>0,a>0,a \[Element]Reals, l \[Element]Reals} Conjugate[(Exp[I a])^(2 l)] //FullSimplify ``

Where Mathematica returns the same thing with no simplification. I told it the assumptions which make it very obvious to just change the sign of the exponent, and I don’t understand why it doesn’t work.

I looked here, but it seems like they have to define their own rules to do this kind of thing. I’m also saw here that you can do `//ComplexExpand //FullSimplify` for this expression, but it doesn’t seem to work in all cases. Why should it be nessecary and why doesn’t FullSimplify do it already? Also, I think ComplexExpand assumes that all variables are real, which was the case in this expression, but isn’t always the case. So how would I do it then?