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I'm trying to work with complexes and I want Mathematica to know that all variables are real unless I explicitly assigned the variable with an I so I wrote:

$Assumptions = Except[I,_] ∈ Reals

It worked fine for simple expressions

f = Exp[-I*a] * a + Exp[-I*b]
Simplify[Conjugate[f]]

Exp[I*a] * a + Exp[I*b]

but for a more complex expression:

g = Exp[-I*a] * a + Exp[-I*b] * b
Simplify[Conjugate[g]]

Exp[-I*a] * a + Exp[-I*b] * b

which is wrong. What can I do about it?

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1 Answer 1

You cannot use Except in $Assumptions like you do.
Just use ComplexExpand which assumes that are variables are real. E.g.:

conj = TrigToExp@ComplexExpand@Conjugate@# &;

Then

  conj[ Exp[-I*a]*a + Exp[-I*b]*b ]

gives

  a*E^(I*a) + b*E^(I*b)
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