I don't manage to make Mathematica understand that x*Conjugate[x]=Abs[x]^2.
For example, let's assume you have :
x*Conjugate[x]^3
How do you make Mathematica simplify it into :
Abs[x]^2*Conjugate[x]^2
?
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Sign up to join this communityTry this:
expr = x*Conjugate[x]^3;
Simplify[expr /. x -> r*Exp[I*t], {r > 0, t > 0}] /.
t :> I*Log[Conjugate[x]/r] /. r -> Abs[x]
(* Abs[x]^2 Conjugate[x]^2 *)
Have fun!
Simplify
, even if Mathematica was considering the proper transformations) $\endgroup$