+226 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:
¯z1+¯z2,¯z1+¯z3,¯z1+¯z4,¯z2+¯z3,¯z2+¯z4,¯z3+¯z4
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 ¯z1+¯z2 is in, your second number corresponds to the quadrant that ¯z1+¯z3 is in, etc.
+23254 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.
