Simplification of conjugate expression with integers

I have a long expression that contains $$(-1)^q$$, where $$q$$ is an integer. I'm taking conjugate of this expression, and Mathematica gives me the term Conjugate[(-1)^q]. And, of course, I'd like to get $$(-1)^q$$.

For the sake of simplicity, I tried to run the following command:

Assuming[Element[q, Integers], Conjugate[(-1)^q]]

And the result was

Conjugate[(-1)^q]

I also tried Simplify and FullSimplify commands; however, the result remained the same.

• Table[-1^q,{q,-3,3}] seems to show that -1^q is -1 for any finite integer q. Even Simplify[-1^q,Element[q,Integers]] knows this is true. So why don't you do that or even do yourexpression/.(-1)^q->-1 or something similar and be get on with the rest of the work you need to do?
– Bill
Commented Aug 22, 2021 at 16:39
• That is a great idea! Thank you! Commented Aug 22, 2021 at 16:48
• ComplexExpand is also useful in this case, Simplify[ComplexExpand[Conjugate[(-1)^q]], Element[q, Integers]]
– I.M.
Commented Aug 23, 2021 at 4:38

Here are 3 ways to get the result you seek (perhaps you were not using the correct syntax)

Assuming[Element[q, Integers], Refine[Conjugate[(-1)^q]]]
(* (-1)^q *)

Assuming[Element[q, Integers], Simplify[Conjugate[(-1)^q]]]
(* (-1)^q *)

Assuming[Element[q, Integers], FullSimplify[Conjugate[(-1)^q]]]
(* (-1)^q *)


Note that Refine is a more specialist version of Simplify, just applying the assumption.

• Thank you very much! Commented Aug 22, 2021 at 16:45