Is this what you wanted?
expr = E^(-((I \[Beta]β)/2)) p (Cos[\[Alpha]Cos[α/2] (Cos[\[Theta]]^2Cos[θ]^2 + Sin[\[Theta]]^2Sin[θ]^2 Sin[\[Phi]]Sin[ϕ] (-I Cos[\[Phi]]Cos[ϕ] + Sin[\[Phi]]Sin[ϕ])) +
E^(I \[Beta]β) Sin[\[Alpha]Sin[α/2] (Cos[\[Theta]]^2Cos[θ]^2 + Sin[\[Theta]]^2Sin[θ]^2 Sin[\[Phi]]Sin[ϕ] (I Cos[\[Phi]]Cos[ϕ] + Sin[\[Phi]]Sin[ϕ])))
expr /. Complex[x_, y_] :> Complex[x, -y]
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]])))
expr /. Complex[x_, y_] :> Complex[x, -y]
Is this what you wanted?
expr = E^(-((I β)/2)) p (Cos[α/2] (Cos[θ]^2 + Sin[θ]^2 Sin[ϕ] (-I Cos[ϕ] + Sin[ϕ])) +
E^(I β) Sin[α/2] (Cos[θ]^2 + Sin[θ]^2 Sin[ϕ] (I Cos[ϕ] + Sin[ϕ])))
expr /. Complex[x_, y_] :> Complex[x, -y]
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]])))
expr /. Complex[x_, y___]y_] :> -Complex[x, -y]
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]])))
expr /. Complex[x_, y___] :> -Complex[x, y]
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]])))
expr /. Complex[x_, y_] :> Complex[x, -y]
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]])))
expr /. Complex[x__]Complex[x_, y___] :> -Complex[x]Complex[x, y]
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]])))
expr /. Complex[x__] :> -Complex[x]
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]])))
expr /. Complex[x_, y___] :> -Complex[x, y]