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complex - How do I make Conjugate behave more consistently?


Sometimes Conjugate distributes. Sometimes it doesn't. Look:


Conjugate[a b]
(* Conjugate[a b] *)

Conjugate[2 a b]
(* 2 Conjugate[a b] *)   (*'2' pulled out*)

Conjugate[a (b + c)]

(* Conjugate[a (b + c)] *)

Conjugate[a (b + 2 c)]
(* Conjugate[a] (Conjugate[b] + 2 Conjugate[c]) *)  (* Distributed! *)

Conjugate[a (b + c (d + e))]
(* Conjugate[a (b + c (d + e))] *)




  1. Why is Conjugate behaving like this (that is, inconsistently)?




  2. Is there a switch I can toggle that prevents Conjugate from doing stuff willy nilly? I don't mind if Conjugate[2 a b] stays Conjugate[2 a b]. It's more consistent that way.





Answer



list = {a b, 2 a b, a (b + c), a (b + 2 c), a (b + c (d + e))};

If you never want Conjugate to distribute, use Inactive



Inactive[Conjugate] /@ list

enter image description here


If you want Conjugate to always distribute


conj[expr_] := 
 ComplexExpand[expr, Variables@Level[expr, {-1}], 
   TargetFunctions -> Conjugate] // Simplify

conj@*Conjugate /@ list


(*  {Conjugate[a] Conjugate[b], 2 Conjugate[a] Conjugate[b], 
 Conjugate[a] (Conjugate[b] + Conjugate[c]), 
 Conjugate[a] (Conjugate[b] + 2 Conjugate[c]), 
 Conjugate[a] (Conjugate[b] + Conjugate[c] (Conjugate[d] + Conjugate[e]))}  *)

If any variables are Reals, say a and c, then use Simplify


Simplify[%, Element[{a, c}, Reals]]

(*  {a Conjugate[b], 2 a Conjugate[b], a (c + Conjugate[b]), 
 a (2 c + Conjugate[b]), a (Conjugate[b] + c (Conjugate[d] + Conjugate[e]))}  *)

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