What is the importance of Act 1 Scene 2 to the audience's image of Claudius in Shakespeare's "Hamlet"

At the beginning of Act 1 Scene 2 Claudius is making a speech at his brother's funeral. This is most important as a first impression of him. The speech is clearly structured in three parts, he talks about the death of the king, his marriage to the queen and the foreign problems of the state. In these three sections it seems at first, as he speaks of his brother's death he is trying to tell the people …

…out to the reader there is that Claudius is making a grab for power shown in his concentration on the foreign policies trying to distract from his lust for power, along with his marriage to the queen giving the change in leadership a smoother and more acceptable feel. He also down plays the death of the formal king so that he can redirect the people's attention to his plans and the problems of the state.