Consider the complex numbers in the following picture, as well as the line segments connecting them to the origin:

Here's a list of pairwise sums of the conjugates of these complex numbers:

\[\overline{z}_1+\overline{z}_2, \overline{z}_1 + \overline{z}_3, \overline{z}_1 + \overline{z}_4, \overline{z}_2 + \overline{z}_3, \overline{z}_2 + \overline{z}_4, \overline{z}_3 + \overline{z}_4.\]

Find the number of the quadrant each of these pairwise sums is in, and answer with the ordered list, such that your first number corresponds to the quadrant that is in, your second number corresponds to the quadrant that is in, etc.

If need be, check part (a) for the standard labelling of the quadrants.

Guest Apr 11, 2019