Now that we've progressed this far, there is one question left unanswered...
So far we've been determining neutral current as though all three loads are connected to the same point on the neutral conductor. However, there are many instances where the loads are not connected at the same point. Referring to the diagram below, the neutral current In(3) will be the same. That of In(1) should be obvious. So what is the magnitude and phase angle of In(2)?
My deductive reasoning says it is equal in magnitude but opposite in phase angle (i.e. 180?) to In(3). I leave it to you guys to prove (or disprove)!