On the number of roots for harmonic trinomials

Abstract

In this manuscript we study the counting problem for harmonic trinomials of the form aζ n + bζ m + c = 0, where n, m ∈ 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 [1].