complex angle

Consider the following, you first go 6 steps in the 1 direction and then 3 in the i direction:

So you divide the corresponding complex number by the total number of steps to get the complex angle.  Note that any similar triangle to this one in the same quadrant, like say (10+5*i)/15 equals the same complex angle. Also note that the complex angle preserves the quadrant the triangle is in. For negative x and positive y, for example, the complex angle will always be of the form -a+b*i, and so on for the four quadrants.