In their groundbreaking work, Khavinson and Świa̧tek proved Wilmshurst’s conjecture, establishing a sharp upper bound on the number of zeros of harmonic polynomials of the form \(h(z)-\overline{z}\) , where h(z) is an analytic polynomial of degree greater than one. Recently, Dorff et al. determined the number of zeros, while Liu et al. identified the compact region containing all zeros of harmonic trinomials. In this article, our research takes a leap further in identifying the precise compact region encompassing all zeros of general harmonic polynomials. Moreover, we utilize the harmonic analog of the argument principle to explore the distribution of zeros of these polynomials, offering insightful examples for clarification.
