MathDB
Complex Numbers

Source: 1991 National High School Mathematics League, Exam One, Problem 11

February 26, 2020
complex numbers

Problem Statement

For two complex numbers z1,z2z_1,z_2 satisfy that ∣z1∣=∣z1+z2∣=3,∣z1−z2∣=33|z_1|=|z_1+z_2|=3,|z_1-z_2|=3\sqrt3, then log⁡3∣(z1z2‾)2000+(z1‾z2)2000∣=\log_3|(z_1\overline{z_2})^{2000}+(\overline{z_1}z_2)^{2000}|=________.
Back to ProblemsView on AoPS