## Theses and Dissertations

#### Abstract

This thesis studies complex harmonic polynomials of the form $f(z) = az^n + b\bar{z}^k+z$ where $n, k \in \mathbb{Z}$ with $n > k$ and $a, b > 0$. We show that the sum of the orders of the zeros of such functions is $n$ and investigate the locations of the zeros, including whether the zeros are in the sense-preserving or sense-reversing region and a set of conditions under which zeros have the same modulus. We also show that the number of zeros ranges from $n$ to $n+2k+2$ as long as certain criteria are met.

MS

#### College and Department

Physical and Mathematical Sciences; Mathematics

2021-12-06

Thesis

#### Handle

http://hdl.lib.byu.edu/1877/etd11972

#### Keywords

harmonic polynomials, zeros, Fundamental Theorem of Algebra

english

COinS