This sentence if you breaks into words, it consists of: 你(ni)=you/已经(yijing)=have,already/征服(zhengfu)=to conquer/我(wo)=me/了(le=a particle). I think in this context the sentence should be translated into: You have persuaded me (by something “you” have done). Is this what you want to know? 🙂 Have a nice day.