JohnDenker
commented
9 years ago Remark: The fundamental issue is not complex exponentials per se, but rather complex numbers in general. Complex numbers have been scrubbed from the book. This is obviously intentional. This sort of decision is not to be changed lightly.
Possibly marginally relevant background information: Complex numbers are covered by the Common Corpse standards, as something "all" students should know for "college and career readiness". http://www.corestandards.org/Math/Content/HSN/CN/ Not that that means very much. With such a standard plus a dollar, you can buy something at the dollar store (unless they charge tax).
Additional observation: This decision affects a lot more than chapter 32. If students do reliably know about complex numbers, it simplifies a lot of other stuff, including 2D rotation of mechanical objects.
The obvious counterargument is: The more math you assume, the more trouble you cause for students who don't know the math ... and for their teachers.
From Bill Ashmanksas: I suppose this would be wildly controversial, but I think that Chapter 32 might be easier to follow if you introduced complex exponentials, then introduced the resistive voltage divider for a sinusoidal input, then showed the low-pass and high-pass filters as voltage dividers in which resistance is generalized to impedance, using complex numbers for impedances. You already discuss adding phasors; for people who have seen deMoivre's formula, the equation may be a nice supplement for the phasor diagram. (Manipulating complex numbers and representing them on the complex plane in rectangular and polar form appears to be part of the Common Core Standards.)