Is the Hijab mandatory?

According to my (limited) knowledge, the Koran is unclear on exactly how to dress, it just has the basic point of dressing conservatively and not showing off your beauty right? The question is whether or not a woman's hair is part of her physical attractiveness. I would say that it is, so if you take the dressing conservatively thing seriously, you should cover up. But it's a matter of personal opinion. Each woman should be allowed to make her own choices, and it will show in her character, and men can judge them on their decisions.