What do you think if I start seeing my ex-friends ex-girlfriend?
It sounds complicated. Why do you want to date her?
Revenge. I hate her and my friend betrayed me by dating such a bitch
Dating someone out of revenge is only going to lead to more problems in the future. Not only are you leading on the girl, but if there was ever any hope of you and your friend talking again, you are blowing that as well. Think through your actions before you do something you might regret.
Thoughts don't kill people. I don't care I'll prove her wrong.
Well, if you hated her and your friend betrayed you, wouldn't you want nothing to do with them anymore? If you were to get back involved with them, you have a lot more to lose, like time, money, and very likely your mental health. It is probably best to let bygones be bygones.