How does this quote reveal Hamlet's character and what is the significance of it?
Act IV Scene 3
"In heaven: send thither to see: if your messenger find him not there, seek him i' the other place yourself"
Hamlet's words echo the spiritual crisis in the play. Earlier, Hamlet refused to kill Claudius at prayer, fearing that it might send him to heaven. Here, he mocks the King spiritually and politically.
In Act I, the Ghost, trapped in Purgatory, presents Hamlet with a task: revenge him. But, according to Christian theology, revenge is a sin capable of sending the avenger to hell. So, how does Hamlet honor his father's request: how can he send the Ghost and himself to heaven and Claudius to hell? Can it be done? Or, will Hamlet join Claudius in hell for committing revenge?
In this quote, Hamlet shows no remorse for killing Polonius. He uses his dead body as bait, calling out the King spiritually. He wants Claudius to send a messenger to see if Polonius is in heaven. Notice that Claudius cannot go to heaven himself: he must send a messenger there.
Hamlet knows that Denmark is full of spies, that Claudius has used Polonius to spy on him. As such, Claudius should send more spies to find Polonius' body. It is bold-faced mockery of the police-state politics of Claudius' reign. Knowing that Claudius has no messengers that can go to heaven, Hamlet is using spirituality to gain the upper hand here--Hamlet has a heavenly messenger in his father's Ghost.
The second part of the statement foreshadows Hamlet's plan for the King: he wants to send him to hell. This statement backfires, as Claudius realizes that Hamlet is not so much mad, but a violent threat to his throne. As such, Claudius sentences Hamlet to execution in England. Later, he will use Laertes and poison to enact his own revenge against the Prince.
All in all, this statement is both a ironic spiritual baiting and a foreshadowing of the fate of both men.
In this scene, King Claudius is trying to get Hamlet to tell him where the body of Polonius is hidden. Hamlet had killed Polonius (while Polonius was behind the arras) and has now hidden the body.
To me, this shows that Hamlet is really quite full of hate for the king. He is, essentially, telling him to go to hell. He is saying that Polonius is in heaven. And if he is not in heaven, he is in hell and Claudius should go there himself to find Polonius. The lines show me that Hamlet is angry and full of hate and does not really care if he makes the king mad at him.