MathDB
2015 BMT Spring Analysis P1

Source:

January 20, 2022
complex numbersinequalitiesalgebra

Problem Statement

Suppose z0,z1,…,zn−1z_0,z_1,\ldots,z_{n-1} are complex numbers such that zk=e2kπi/nz_k=e^{2k\pi i/n} for k=0,1,2,…,n−1k=0,1,2,\ldots,n-1. Prove that for any complex number zz, ∑k=0n−1∣z−zk∣≥n\sum_{k=0}^{n-1}|z-z_k|\ge n.
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