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I'm trying to take absolute value squared of certain objects. Say I have 

y=alpha

and I know that |alpha|^2 = alpha*Conjugate[alpha].

How do I take Abs[y]^2 without assigning a numerical value to alpha in mathematica?

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  • $\begingroup$ Depending on the form of the output desired: Clear[alpha]; Abs[alpha]^2 // ComplexExpand[#, {alpha}] & or Abs[alpha]^2 // ComplexExpand[#, {alpha}, TargetFunctions -> Conjugate] & $\endgroup$ – Bob Hanlon Apr 8 at 23:15
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α = αr + I*αi;
Abs[α]^2 // ComplexExpand

αi^2 + αr^2

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y[alpha_] := Abs[alpha]^2

ComplexExpand[y[a - I*b]]

a^2 + b^2
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