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15
15
Part of
2015 Math Prize for Girls Problems
Problems
(1)
Math Prize 2015 Problem 15
Source:
9/22/2015
Let
z
1
z_1
z
1
,
z
2
z_2
z
2
,
z
3
z_3
z
3
, and
z
4
z_4
z
4
be the four distinct complex solutions of the equation
z
4
−
6
z
2
+
8
z
+
1
=
−
4
(
z
3
−
z
+
2
)
i
.
z^4 - 6z^2 + 8z + 1 = -4(z^3 - z + 2)i.
z
4
−
6
z
2
+
8
z
+
1
=
−
4
(
z
3
−
z
+
2
)
i
.
Find the sum of the six pairwise distances between
z
1
z_1
z
1
,
z
2
z_2
z
2
,
z
3
z_3
z
3
, and
z
4
z_4
z
4
.