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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$\endgroup$
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α = αr + I*αi;
Abs[α]^2 // ComplexExpand
αi^2 + αr^2
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$\endgroup$
y[alpha_] := Abs[alpha]^2
ComplexExpand[y[a - I*b]]
a^2 + b^2
Clear[alpha]; Abs[alpha]^2 // ComplexExpand[#, {alpha}] &orAbs[alpha]^2 // ComplexExpand[#, {alpha}, TargetFunctions -> Conjugate] &$\endgroup$ – Bob Hanlon Apr 8 '19 at 23:15