Should I get in relationship with roommate's friend?

The situation you are in honestly sucks. Do you plan to have a serious relationship? Is it just a winter fling or maybe a relationship that will maybe last a couple months? If you don't plan to have anything too serious with this girl, then you should probably stop talking to her. You will only jeopardize your friendship and trust with Alexander. If you really like this girl and feel she is different from others, then go for it. If you think it will head somewhere good, Alex will just have accept the idea. If things don't work out between you and this girl, you have to keep in mind that Alex will hold a grudge against you for some time.