On the number of roots for harmonic trinomials

In this manuscript we study the counting problem for harmonic trinomials of the form a zeta(n) + b (zeta) over bar (m) + c, where n, m is an element of 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]. (C) 2022 The Author(s). Published by Elsevier Inc.Peer reviewe