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BMT 2021 General Tiebreaker p4
BMT 2021 General Tiebreaker p4
Source:
September 27, 2023
complex numbers
algebra
Problem Statement
Let
z
1
z_1
z
1
,
z
2
z_2
z
2
, and
z
3
z_3
z
3
be the complex roots of the equation
(
2
z
−
3
z
‾
)
3
=
54
i
+
54
(2z -3\overline{z})^3 = 54i+54
(
2
z
−
3
z
)
3
=
54
i
+
54
. Compute the area of the triangle formed by
z
1
z_1
z
1
,
z
2
z_2
z
2
, and
z
3
z_3
z
3
when plotted in the complex plane.
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