  The aim of this note is to give a surprising symmetry property of some
harmonic 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 $z_i$, and
such that $\Arg(P(z))=\theta$, form a regular $n$-gon, where $n$ is the degree
of $P$.
