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avatar+221 

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
 #1
avatar+221 
0

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

 Aug 8, 2020
 #2
avatar+21957 
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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

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