Final answer:
The excerpt provided doesn't pertain to Duke Orsino, but Orsino's character in Twelfth Night is typically melancholic and pensive.
Step-by-step explanation:
This excerpt from Shakespeare’s Twelfth Night doesn’t specifically describe Duke Orsino, as it references Hamlet and his emotional state, rather than Orsino’s. However, when we look at Twelfth Night, Orsino is often portrayed as melancholic and pensive, particularly in his obsessive love for Olivia, and the way he indulges his emotions with music and lengthy speeches about love. Consequently, the correct answer regarding Duke Orsino based on his character in Twelfth Night is a) "He is melancholic and pensive."