Zeros of a two-parameter family of harmonic quadrinomials

Abstract

In this paper, we determine the number of zeros and the zero inclusion regions of a two-parameter family of harmonic quadrinomials. We also determine a curve that separates sensepreserving and sense-reversing regions for these families of quadrinomials. Our work makes practical and effective use of the work of Wilmshurst, Khavinson, Dehmer, and also Bezout’s Theorem in the plane.