Some texts/materials have the neutral current In traveling in the same direction as the phase currents, such that the phase currents and neutral current all flow towards the neutral connection point of a wye. I believe the NCEES PE practice exam uses this reference for the neutral point. So if that's the case, then basically since all the phase currents and neutral current are traveling INTO the same node:
Ia + Ib + Ic + In = 0
(In this problem, Ic is just 0)
I prefer referencing the neutral current as flowing out of the neutral connection point, and therefore flowing in the opposite direction than that of the phase currents. So then in my case, the phase currents flow into the neutral connection point of the wye, and the neutral current flows out of the neutral connection point. So that means I prefer:
Ia + Ib + Ic - In = 0
In = Ia + Ib + Ic
In either case, this is just simply KCL at the neutral connection point regardless of how you want to reference the neutral current's flowing direction.
The neutral current's magnitude will be the same regardless of which direction you reference having it flow. Only the angle will change. If you want to flip the neutral current's direction or any phasor's direction, you just simply add +180 degrees to its phase angle (which is equivalent to making the phasor itself negative or multiplying the phasor by -1).
Attached is my work for this problem (this was problem 108 in the previous version of the NCEES practice power exam).
