global-journal-of-science-frontier-research-f-mathematics-decision Global Journal of Science Frontier Research - F: Mathematics & Decision 0975-5896 2249-4626 Global Journals Publishing Group Incorporated 83695 Exploring Repetitive Integer Patterns in the Complex Roots of Homogeneous Polynomials Patterns in Polynomial Roots and Imaginary Sets StreidlDerek UNITED STATES, Indiana University East 20 01 2025 24 F2 1 7

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 𝜸𝜸 values starting at n=3, this pattern is observed for entire sets of multiples.

 imaginary iterative zeros patterns homogeneous polynomials number theory polynomial roots polynomial zeroes. Full Text

In similar 4th 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 𝛾𝛾 values starting at n=3, this pattern is observed for entire sets of multiples.