# Conjugate[a/b + c/d]

Trying to obtain the result of Conjugate[a/b+c/d] only gives the same result. As such, I use Refine as:

Refine[
Conjugate[a/b + c/d], a ∈ Complexes && b ∈ Reals && c ∈ Reals && d ∈ Complexes]


with the output

Conjugate[a/b + c/d]

Funny thing is that if I try

Refine[Conjugate[a/b + c/d],a ∈ Reals && b ∈ Reals && c ∈ Reals && d ∈ Reals]


I get

a/b + c/d

or, if I try

Refine[Conjugate[a/b + c], a ∈ Complexes && b ∈ Reals && c ∈ Reals]


I get

c + Conjugate[a]/b

As soon as I have two fractions inside Conjugate], with any of the elements as Complex, I do not get the conjugate of each element, which is my obvious goal. Any reason why this happens?

I manage to get the desired result in this case for example:

In[252]:= Distribute@
Conjugate[fc (2 E^((2 I fc \[Pi] (R1 + R2))/\[ConstantC]) mu1 c)]

Out[252]= 2 E^(-((2 I \[Pi] Conjugate[fc (R1 + R2)])/
Conjugate[\[ConstantC]])) Conjugate[c fc mu1]

In[253]:= FullSimplify[%]

Out[253]= 2 E^(-((2 I fc \[Pi] (R1 + R2))/\[ConstantC])) fc Conjugate[
c] Conjugate[mu1]

In[254]:= TraditionalForm[%]

Out[254]//TraditionalForm= 2 fc c^\[Conjugate] mu1^\[Conjugate] E^(-((2 I \[Pi] fc (R1+R2))/\[ConstantC]))


However as soon as I try to do it for

Distribute@ Conjugate[ fc (2 E^((2 I fc [Pi] (R1 + R2))/[ConstantC]) mu1 c + E^((4 I fc [Pi] R1)/[ConstantC]) mu2 d)]

the same series of commands produces only

fc (2 c E^((2 I fc \[Pi] (R1+R2))/\[ConstantC]) mu1+d E^((4 I fc \[Pi] R1)/\[ConstantC]) mu2)^\[Conjugate]


not what I would expect the result to be

2 fc c^\[Conjugate] mu1^\[Conjugate] E^(-((2 I \[Pi] fc (R1+R2))/\[ConstantC])) + fc d^\[Conjugate] mu2^\[Conjugate] E^(-((4 I \[Pi] fc R1)/\[ConstantC]))

• Do avoid using C and D for this, as they are reserved symbols. May 24, 2016 at 13:37
• Yes, it was just an example. I actually have more complicated terms than A, B, C or D. Thanks for the quick input! May 24, 2016 at 13:52
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– user9660
May 24, 2016 at 13:59
• You should edit the question to fix the caps, it is distracting from the issue. I suspect the problem is simply that the result you "expect" is regarded as more complicated than the result you get. May 24, 2016 at 14:30
• Conjugate[a/b + c/d] returns Conjugate[a/b + c/d]. What else did you expect? Your error is in using capital C and D. They are reserved, and Mma could not understand you. May 24, 2016 at 14:47

## 2 Answers

I find that getting the answer I want with this type of expression requires the use of a range of techniques. In this case, I would use

ComplexExpand[Conjugate[a/b + c/d], {a, d},  TargetFunctions -> Conjugate]


giving

Conjugate[a]/b + c/Conjugate[d]


You probably need to distribute every product over sums in your expression in order for Conjugate to propagate properly:

distributeProducts[expr_] :=
Replace[expr, t : Times[___] :> Distribute[t], {0, \[Infinity]}]

distributeProducts@
Conjugate[
fc (2 c E^((2 I fc \[Pi] (R1 + R2))/\[ConstantC]) mu1 +
d E^((4 I fc \[Pi] R1)/\[ConstantC]) mu2)]