Problem

Source: 2023 China South-east Mathematical Olympiad Grade 11 P2 CSMO

Tags: complex numbers, algebra



For a non-empty finite complex number set A, define the "Tao root" of A as |zAz|. Given the integer n3, let the set Un={cos2kπn+isin2kπn|k=0,1,...,n1}.Let an be the number of non-empty subsets in which the Tao root of Un is 0 , bn is the number of non-empty subsets of Un whose Tao root is 1. Compare the sizes of nan and 2bn.