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Sibling curves 3: imaginary siblings and tracing complex roots

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Visualizing complex roots of a quadratic equation has been a quest since the inception of the Argand plane in the 1800s. Many algebraic and numerical methods exist for calculating complex roots of an equation, but few visual methods exist. Following on from papers by Harding and Engelbrecht (A. Harding and J. Engelbrecht, Sibling curves and complex roots 1: looking back, Int. J. Math. Educ. Sci. Technol. 38(7) (2007), pp. 963-974; A. Harding and J. Engelbrecht, Sibling curves and complex roots 2: looking ahead, Int. J. Math. Educ. Sci. Technol. 38(7) (2007), pp. 975-985), where the existence and properties of sibling curves for the well-known functions were described, we introduce imaginary sibling curves. We then focus on the domain curves of siblings and their imaginary counterparts to trace and visualize the complex roots.
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Keywords: complex numbers; complex roots; sibling curves; visualizing roots

Document Type: Research Article

Affiliations: Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa

Publication date: 2009-01-01

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