Hello everyone. Is it possible to get z Conjugate[z]=(Abs[z])^2 without defining z=a+I b? To do this I need to define z as a symbolic complex number, but this procedure is unclear for me.
Thank you in advance.
Use ComplexExpand:
ComplexExpand
ComplexExpand[z Conjugate[z], z, TargetFunctions -> {Abs}] (* Abs[z]^2 *)
You can do it with replacement rules:
a*b*Conjugate[a] /. z_*Conjugate[z_] :> Abs[z]^2 a*b*Conjugate[a] /. Conjugate[z_] :> Abs[z]^2/z
