MathDB
Complex number inequality

Source: Romanian District Olympiad 2023 10.3

March 11, 2023
complex numbersinequalities

Problem Statement

Let n⩾2n\geqslant 2 be an integer. Determine all complex numbers zz{} which satisfy ∣zn+1−zn∣⩾∣zn+1−1∣+∣zn+1−z∣.|z^{n+1}-z^n|\geqslant|z^{n+1}-1|+|z^{n+1}-z|.
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