Visualizing the Complex Roots of Quadratic and Cubic Polynomial Functions in Three Dimensions

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Acknowledgments

The author thanks to Dr. Mark L. Daniels for encouraging him to pursue this problem in its various aspects and is grateful to Dr. Mark L. Daniels, Dr. Solomon Manukure, Dr. Hector E. Lomeli, and Carter Smith for their helpful discussions on the topic. The author also thanks to the anonymous reviewer whose comments/suggestions helped improve and clarify this article.

Summary

In this article, we have calculated the respective reduced complex domains of quadratic and cubic functions that would yield a real range. Using this approach, we can graphically visualize and obtain the complex roots of any quadratic and cubic function in MATLAB.

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Notes on contributors

Aniket Sanghi

Aniket Sanghi ([email protected], ORCID 0000-0002-1838-4757) is a junior undergraduate student at the University of Texas at Austin where he is majoring in Astronomy and Physics. His goal is to lead the scientific priorities of the next generation of telescopes by designing, proposing, and conducting large-scale, high-impact research programs and surveys, to push the boundaries of science that the astronomy community can accomplish. He also aims to support and mentor underrepresented minorities in STEM.