Resumen de Sibling curves 3: imaginary siblings and tracing complex roots

Ansie Harding, Johann Engelbrecht

• 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.