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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.

Aug 7, 2020

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I have figured out the answer which is, 3,3,4,3,2,4

Aug 8, 2020
#2
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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:

z1  =  1 + 5i     z2  =  -4 - i     z3  =  -3 + 4i     z4  =  5 - 3i

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

Aug 8, 2020