I'm trying to take complex conjugate of some terms in a function. I tried this

α = αr + I*αi;
β = βr + I*βi;
$Assumptions = Element[αr, Reals];
$Assumptions = Element[αi, Reals];
$Assumptions = Element[βr, Reals];
$Assumptions = Element[βi, Reals];

b0 = (T0*(β - R1*Exp[2*I*(w*l/c)]*α)/((R0*beta - Conjugate[α]) - 
       R1*Exp[2*I*(w*l/c)]*(R0*α - Conjugate[β])))*fw

but the output I get is

(fw T0 (-E^(((2 I l w)/c)) R1 (I αi + αr) + I βi + βr))/(
  beta R0 + I Conjugate[αi] - Conjugate[αr] - 
    E^((2 I l w)/c) R1 (R0 (I αi + αr) + I Conjugate[βi] - Conjugate[βr]))

I don't understand what to do to get rid of the terms containing Conjugate, e.g. Conjugate[αi] etc.

  • $\begingroup$ Use $Assumptions = Element[{αr, αi, βr, βi}, Reals] and then don't forget to FullSimplify your expression b0 in order to apply these assumptions. $\endgroup$
    – Roman
    Apr 9, 2019 at 8:56
  • 5
    $\begingroup$ $Assumptions only affects functions that have the Assumptions option. Conjugate is not one of these, but e.g. Simplify is, which you can apply to your expression. Also look up ComplexExpand. $\endgroup$
    – Szabolcs
    Apr 9, 2019 at 9:17
  • $\begingroup$ ComplexExpand might also be worth a read. $\endgroup$ Apr 10, 2019 at 6:20


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