Mathematica Help: FullSimplify does not use conjugate identities

[Schwinger]

FullSimplify fails to recognize that:
a*Conjugate + b*Conjugate[a] = 2 Re[a*b]
I have some very complex equations that could be simplified greatly if Mathematica could recognize this simple identity (and that a*Conjugate - b*Conjugate[a] = 2 Im[a*b]).

I simply cannot figure out how to get it to recognize this, so I would appreciate some feedback!

 

[eLiu]

FullSimplify fails to recognize that:
a*Conjugate + b*Conjugate[a] = 2 Re[a*b]
I have some very complex equations that could be simplified greatly if Mathematica could recognize this simple identity (and that a*Conjugate - b*Conjugate[a] = 2 Im[a*b]).

I simply cannot figure out how to get it to recognize this, so I would appreciate some feedback!

I'm not a mathematica user, but could force it to convert everything to exponential form? I find this often helps in maple.

 

[CP5670]

FullSimplify misses a lot of obvious things like this. You often need to take its output and do it yourself.