Applying Complex Numbers to Alternating Current (AC) Circuits

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: