# A symmetry property of some harmonic algebraic curves - Mathematics > General Mathematics

Abstract: The aim of this note is to give a surprising symmetry property of someharmonic algebraic curves: when all the roots $z i$ of a complex polynomial $P$lie on the unit circle $\U$, the points of $\U$ different from the $z i$, andsuch that $\ArgPz=\theta$, form a regular $n$-gon, where $n$ is the degreeof $P$.

Author: Jean-Christophe Aval LaBRI, Jean-François Marckert LaBRI

Source: https://arxiv.org/