Is this what you wanted?

    expr = E^(-((I \[Beta])/2)) p (Cos[\[Alpha]/2] (Cos[\[Theta]]^2 + Sin[\[Theta]]^2 Sin[\[Phi]] (-I Cos[\[Phi]] + Sin[\[Phi]])) + 
        E^(I \[Beta]) Sin[\[Alpha]/2] (Cos[\[Theta]]^2 + Sin[\[Theta]]^2 Sin[\[Phi]] (I Cos[\[Phi]] + Sin[\[Phi]])))

![Mathematica graphics](https://i.sstatic.net/3nscW.png)

    expr /. Complex[x__] :> -Complex[x]

![Mathematica graphics](https://i.sstatic.net/4FjlG.png)