# Replace $z z^*$ by $|z|^2$

I have a long expression involving different complex numbers. I want to force Mathematica to replace z Conjugate[z] by Abs[z]^2 without using polar coordinates in the whole expression. For example,

z w Conjugate[z] Conjugate[w] + Conjugate[z] w + z^2


should just be 'simplified' to

Abs[z]^2 Abs[w]^2 + Conjugate[z] w + z^2


One way is to use a repeatedly applied rule

z w Conjugate[z] Conjugate[w] + Conjugate[z] w + z^2 //. a_ Conjugate[a_] :> Abs[a]^2

z^2 + Abs[w]^2 Abs[z]^2 + w Conjugate[z]


The FullSimplify function knows how to do that:

FullSimplify[z Conjugate[z]]

 Abs[z]^2