Complex Analysis with Mathematica, Simplify, Absolute value

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


?

• 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) – mmeent May 24 '18 at 10:29

expr = x*Conjugate[x]^3;