This is my final result.You didn't finish your work, so I can't compare to my final result.
You have a lot of unnecessary algebra which invites mistakes as a result of including the 3+j2 branch between nodes 1 and 2. That branch is connected in parallel with a voltage source, and therefore has no effect on the voltages at node 1 and node 2.
It would probably be worth while to eliminate that branch and do it all over again.
by Jake Hertz
by Duane Benson
by Jake Hertz
by Jake Hertz