Perhaps this was left as an exercise for the reader? It seems to follow quite closely from the same intuition: after you have averaged the points on the imaginary plane you get a point that you can can represent as (r,theta). Theta is the phase portion. It's just the direction of the constructively interfering peak.
The phase portion isn't actually just the imaginary part, it's just the piece of information lost when one goes from real+imag -> magnitude, i.e. it's the argument of the complex number.