# Complex conjugate of real number [duplicate]

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.

• Use $Assumptions = Element[{αr, αi, βr, βi}, Reals] and then don't forget to FullSimplify your expression b0 in order to apply these assumptions. Apr 9, 2019 at 8:56 • $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. Apr 9, 2019 at 9:17
• ComplexExpand might also be worth a read. Apr 10, 2019 at 6:20