0
$\begingroup$

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 

?

$\endgroup$
1
  • $\begingroup$ By most metrics the second expression is "less simple" than the second. (Hence the first expression would be prefered by Simplify, even if Mathematica was considering the proper transformations) $\endgroup$
    – TimRias
    May 24, 2018 at 10:29

1 Answer 1

1
$\begingroup$

Try 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!

$\endgroup$

Your Answer

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

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