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


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

  • 1
    $\begingroup$ 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? $\endgroup$
    – Bill
    Commented Aug 22, 2021 at 16:39
  • $\begingroup$ That is a great idea! Thank you! $\endgroup$
    – Svetlana
    Commented Aug 22, 2021 at 16:48
  • $\begingroup$ ComplexExpand is also useful in this case, Simplify[ComplexExpand[Conjugate[(-1)^q]], Element[q, Integers]] $\endgroup$
    – I.M.
    Commented Aug 23, 2021 at 4:38

1 Answer 1


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.

  • $\begingroup$ Thank you very much! $\endgroup$
    – Svetlana
    Commented Aug 22, 2021 at 16:45

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.