Lesson Notes.
The goal of this pullout is to provide a
convincing application of complex
numbers. Students will learn something
about electricity and review complex
numbers and trigonometry. It would be
good if they could do graphs of trig
functions by hand, and calculate quickly
the trig functions of the regular angles by
using a 45° right triangle, and a 30°, 60°
right triangle, and the coordinates on the
axes–and, know the general shapes of the
graphs of the trig functions.
For this pullout, students should simply
read the article, taking notes, and doing
the activities. Then they can work the
exercises. Of course, the teacher may
allow students access to the answers or
not.
A teacher can check with a science teacher
for demonstrations, and suggest term papers
or projects for students. For example, there
is a small laboratory type rotary generator
available in catalogs (Sargent Welch Scientific
Co.). Students might like to experiment with
a multimeter – but be careful with the
milliamp functions. This part of the meter
can be damaged. Naturally, students have
access to wikipedia, which is amazing.
There are in print some nice graphical
representations of complex roots to a
quadratic equation:
