id: 06467661
dt: j
an: 2015e.00546
au: Soto-Johnson, Hortensia
ti: Visualizing the arithmetic of complex numbers.
so: Int. J. Technol. Math. Educ. 21, No. 3, 103-114 (2014).
py: 2014
pu: Research Information Ltd, Burnham, Bucks
la: EN
cc: F50 U70
ut: arithmetic; complex numbers; geometric representation; algebraic
representations; use of technology; visualization
ci:
li: http://www.researchinformation.co.uk/timearch/2014-03/pageflip.html
ab: Summary: The Common Core State Standards Initiative stresses the importance
of developing a geometric and algebraic understanding of complex
numbers in their different forms (i.e., Cartesian, polar and
exponential). Unfortunately, most high school textbooks do not offer
such explanations much less exercises that encourage students to bridge
geometric and algebraic representations. The purpose of this article is
to share Geometerâ€™s Sketchpad labs, where students can unearth a
geometric interpretation of the arithmetic of complex numbers and their
relationship to transformations. With dynamic technologies, students
can discover that (1) addition and subtraction of complex numbers
corresponds to a translation of the complex plane, (2) multiplication
corresponds to a rotation and dilation of the complex plane, and (3)
division of complex numbers corresponds to the composition of a
reflection about the real axis and dilation of the complex plane.
Furthermore, I illustrate how such activities may potentially enrich
classroom dialogue.
rv: