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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.

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    $\begingroup$ 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

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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.

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

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