Showing the Hermitean Adjoint Property for Operators

[QuantumJG]

How would I go about showing:

\hat{A}^{\dagger} + \hat{B}^{\dagger} = \left( \hat{A} + \hat{B} \right) ^{\dagger}

 

[grey_earl]

You could start from the definition of the Hermitean adjoint,
\langle \psi | A^\dagger | \phi \rangle = \langle \phi | A | \psi \rangle^* and use that the complex conjugation is linear,
(a+b)^* = a^* + b^*.