Sibling curves 3: imaginary siblings and tracing complex roots. (English)

Int. J. Math. Educ. Sci. Technol. 40, No. 7, Spec. Iss., 989-996 (2009).

Summary: 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 the authors [ibid. 38, No. 7, 963‒974 2007; ME 2007e.00372); ibid. 38, No. 7, 975‒985 (2007; ME 2007e.00373)], 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.