In this manuscript we study the counting problem for harmonic trinomials of the form $a\zeta^n+b\overline{ \zeta}^m+c$, where $n,m\in \mathbb{ N}$, $n>m$, and $a$, $b$ and $c$ are non-zero complex numbers. As a consequence, we obtain the Fundamental Theorem of Algebra and the Wilmshurst conjecture for harmonic trinomials. The proof of the counting problem relies on the Bohl method introduced in Bohl (1908).
Categories: math.CV