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

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Listed:
  • Harry Wiggins
  • Ansie Harding
  • Johann Engelbrecht

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.

Suggested Citation

  • Harry Wiggins & Ansie Harding & Johann Engelbrecht, 2018. "Visualising Complex Polynomials: A Parabola Is but a Drop in the Ocean of Quadratics," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(6), pages 91-97, December.
    • Handle: RePEc:ibn:jmrjnl:v:10:y:2018:i:6:p:91
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    References listed on IDEAS

    as
    1. Lembke B., 1918. "√ a. p," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 111(1), pages 709-712, February.
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    More about this item

    Keywords

    complex zeroes; complex polynomials;

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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