Darth Vader, formerly known as Anakin Skywalker, had a complex relationship with Obi-Wan Kenobi that evolved significantly over the course of the Star Wars saga. If we consider the context of their duel on Mustafar and the surrounding events, Vader’s questioning likely stems from a combination of regret, anger, and a desire for closure.
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Confrontation and Conflict: During their duel on Mustafar, Anakin's transformation into Darth Vader was complete, and he felt betrayed by Obi-Wan. His questions may reflect his inner turmoil and confusion regarding the choices he made, the actions of his former mentor, and his own feelings of loss and abandonment.
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Death of Padmé: Anakin’s fall to the dark side was heavily influenced by his fear of losing Padmé Amidala. If he were to confront Obi-Wan about Padmé's death, it would likely be an expression of his anger and desperation to understand why he had lost her, as well as to blame Obi-Wan for his role in that death.
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Hidden Children: The revelation of his children (Luke and Leia) becomes a significant factor in Vader's character arc. His questions about their existence could reflect his unresolved feelings of fatherhood and his fears about what his legacy would be. He might seek to understand what was happening in the galaxy and where his children fit into it.
In essence, Vader’s inquiries are driven by deep-seated emotions and unresolved conflicts, making them a key aspect of his character development. This narrative helps to explore themes of loss, betrayal, and redemption that are central to the Star Wars saga.