id: 05676367
dt: j
an: 2010b.00494
au: Harding, Ansie; Engelbrecht, Johann
ti: Sibling curves 3: imaginary siblings and tracing complex roots.
so: Int. J. Math. Educ. Sci. Technol. 40, No. 7, Spec. Iss., 989-996 (2009).
py: 2009
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: H30 F50 I80 R20
ut: sibling curves; complex numbers; complex roots; visualizing roots
ci: ME 2007e.00372; ME 2007e.00373
li: doi:10.1080/00207390903200992
ab: 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.
rv: