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]))
C
andD
for this, as they are reserved symbols. $\endgroup$Conjugate[a/b + c/d]
returnsConjugate[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. $\endgroup$