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 \(\overline{z}_1+\overline{z}_2\) is in, your second number corresponds to the quadrant that \(\overline{z}_1+\overline{z}_3\) is in, etc.

littlemixfan Aug 7, 2020

#2**+1 **

By the way the question is asked, I assume that none of the sums land on an axis.

The easist way to do this is to assign values to each of the complex numbers, such as:

z_{1} = 1 + 5i z_{2} = -4 - i z_{3} = -3 + 4i z_{4} = 5 - 3i

and then find each of the sums, locating the quadrant that contains each of the sums.

geno3141 Aug 8, 2020