Visualising Complex Polynomials: A Parabola Is but a Drop in the Ocean of Quadratics

Harry Wiggins, Ansie Harding and Johann Engelbrecht

Journal of Mathematics Research, 2018, vol. 10, issue 6, 91-97

Abstract: One of the problems encountered when teaching complex numbers arises from an inability to visualise the complex roots, the so-called ”imaginary” roots of a polynomial. Being four dimensional, it is problematic to visualize graphs and roots of polynomials with complex coefficients in spite of many attempts through centuries. An innovative way is described to visualize the graphs and roots of functions, by restricting the domain of the complex function to those complex numbers that map onto real values, leading to the concept of three dimensional sibling curves. Using this approach we see that a parabola is but a singular case of a complex quadratic. We see that sibling curves of a complex quadratic lie on a three-dimensional hyperbolic paraboloid. Finally, we show that the restriction to a real range causes no loss of generality.

Keywords: complex zeroes; complex polynomials (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.ccsenet.org/journal/index.php/jmr/article/download/0/0/37612/38004 (application/pdf)
http://www.ccsenet.org/journal/index.php/jmr/article/view/0/37612 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:10:y:2018:i:6:p:91

Access Statistics for this article

More articles in Journal of Mathematics Research from Canadian Center of Science and Education Contact information at EDIRC.
Bibliographic data for series maintained by Canadian Center of Science and Education ().