I figured it out

(Thanks for responding!)

My instructor was busy disecting each phasor into X and Y values with sin/cos functions and subtracting them. It just didn't make sense until he showed what he was doing with a phasor diagram and finally had a 3-blade propellor drawn on the board. *Now* that made a whole lot more sense! I worked through a few more problems with the diagrams only... and solved them all. Now the original purely-arithmetic method is starting to make sense. Go figure

What I found arbitrary was how he assigned the A, B, & C phase subscripts to the current phasors. I now know it doesn't matter - you get same answers no matter how you do it.

Here is one of the problems. I'll see if I can transcribe the solution and post it up.

Q:

The phase currents in a delta-connected, unbalanced load are 20A, 32A, and 40A. Calculate the three line currents, if all loads are resistors.

A:

52.92A, 62.35A, 45.43A