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Work on symbolic complex numbers - z Conjugate[z]=(Abs[z])^2 ?

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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.

POSTED BY: Gennaro Arguzzi
Answer
2 months ago

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
POSTED BY: Gianluca Gorni
Answer
2 months ago

Use ComplexExpand:

ComplexExpand[z Conjugate[z], z, TargetFunctions -> {Abs}]

(* Abs[z]^2 *)
POSTED BY: Carl Woll
Answer
2 months ago

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