Basic circuit analysis - phase shifting
First apply Kirchhoff's current rule at junction 0. That gives you the current in the 1-0 branch, because you already know the other two currents. Now just trace a path from 0 to 1 algebraically adding voltages. Then you have the answer. That's basically what the first person said.

I think the mistake you're making is that you're assuming zero current in the 1-0 branch. You cannot arbitrarily do so. The branch is not open, it's just that any other connection, it might have, isn't shown.