Exploring Repetitive Integer Patterns in the Complex Roots of Homogeneous Polynomials

Abstract

In similar 4 th degree polynomials, certain roots exhibit a pattern where an integer serves as both a negative factor of the polynomial's constant and the value of the imaginary component of the root. This integer, called the 'negative base multiple,' appears consistently across multiple sets, which we term 'iterative imaginary number sets.' By increasing initial values starting at n=3, this pattern is observed for entire sets of multiples.