If we have two points $z_1=x_1+iy_1$ and $z_2=x_2+iy_2$ in the complex plane and define the relative coordinate $z=z_2-z_1$, we have that the length of $z$ is the Euclidian distance between the points:
But what about the phase of $z$? The best I have been able to come up with is
I kind of expect the answer to be the angle between the points
but I haven't been able to show this.