In the opening of the story, the narrator and Dupin the detective sit in silence for an hour; during this time, the narrator has been "mentally discussing certain topics which had formed matter for conversation between us at an earlier period of the evening," indicating that he is making use of his imagination. It is clear that Dupin, however, is the smartest man in the room, and when the Prefect of Paris arrives, that remains the case. The Prefect's descriptions of the Minister's home enable Dupin to use his well-developed imagination and save himself time when he goes to look for the purloined letter himself.
It could be said that Dupin misuses his imagination; instead of solving the case for the sake of justice, he uses his imagination to hold onto the letter himself until he can claim the fifty thousand franc reward once it has doubled. He takes pride in his intelligence and measures himself against the cleverness of the Minister so that he gets a four-part victory: he outwits the imaginative thief and blackmailer, collects a substantial reward, rescues the damsel in distress, and shows up the Prefect of the police. To cap his victory, he leaves a note in the Minister's home with a clever allusion to an ancient Greek myth that casts the Minster and himself as brothers who are both imaginative and cunning.