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Complex Plane

Source: 1988 National High School Mathematics League, Exam One, Problem 11

February 25, 2020

Problem Statement

On complex plane, path equation of moving point Z1Z_1 is ∣Z1−Z0∣=∣Z1∣|Z_1-Z_0|=|Z_1|, where Z0(Z0≠0)Z_0(Z_0\neq0) is a fixed point. Another moving point ZZ satisfies that ZZ1=−1ZZ_1=-1. Find the path of ZZ and describe its location and shape.
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