Making multiple assumptions.

Questions
1

Hello,

I am trying to find the complex conjugate of E^(- I a e) in Mathematica, but when I enter

Conjugate[Exp[-I a e]]

Mathematica assumes both the variables a and e are real. So far I have been able to make mathematica assume that ONE of them is real by writing

Simplify[Conjugate[Exp[-I a e]], a \[Element] Reals]

so that a is assumed to be real.

So the question is, how do I make Mathematica assume both a and e are real?

Thank you.

2

Try

Simplify[Conjugate[Exp[-I a e]], {a, e} \[Element] Reals]
3

An unnecessarily complicated solutions, posted just to show the generality of using ComplexExpand for such things:

Conjugate[Exp[-I a e]] // ComplexExpand // TrigToExp

Without the final TrigToExp, you’d get as output:

    Cos[a e] + I Sin[a e]