
05676367
j
2010b.00494
Harding, Ansie
Engelbrecht, Johann
Sibling curves 3: imaginary siblings and tracing complex roots.
Int. J. Math. Educ. Sci. Technol. 40, No. 7, Spec. Iss., 989996 (2009).
2009
Taylor \& Francis, Abingdon, Oxfordshire
EN
H30
F50
I80
R20
sibling curves
complex numbers
complex roots
visualizing roots
ME 2007e.00372
ME 2007e.00373
doi:10.1080/00207390903200992
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, 963974 2007; ME 2007e.00372); ibid. 38, No. 7, 975985 (2007; ME 2007e.00373)], where the existence and properties of sibling curves for the wellknown 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.