Abstract by Alexandra Hudson
Zeros of Complex Harmonic Polynomials Part 3: Future Directions
The next step in our research is to develop proof techniques for the general case. In complex analysis we cover Rouche's Theorem which assists with counting and locating zeros of analytic functions. In order to use the harmonic version of Rouche's Theorem, we need to understand the function called the complex dilatation. In this section we are going to explore conjectures we have formed using the complex dilatation.