I am pretty new to Mathematica and these forums have helped me figure out almost everything except for how to simplify complex expressions. I have tried many combinations of complexsimplify and fullsimply and just simplify while also putting in bounds to make sure mathematica knows my variables are real, but I can't get it to spit out a the nicer analytical solution I'm sure exists. Everything is always kept in terms of abs, rather than actually taking the modulus. It seems like these simplifications are very case dependent.
Anyway, here I am trying to simplify this expression, (sorry I don't know how to put it in traditional form here).
Abs[(Sqrt[-(Ay-kF2-q) (Ay+kF2-q)] Sqrt[(kF1-q) (kF1+q)])/(Sqrt[-(Ay-kF2-q) (Ay+kF2-q)] Sqrt[(kF1-q) (kF1+q)] Cos[L Sqrt[(Ay+kF2-q) (-Ay+kF2+q)]]-I (Sqrt[kF1^2] Sqrt[kF2^2]+(Ay-q) q) Sin[L Sqrt[-Ay^2+kF2^2+2 Ay q-q^2]])]^2