INTALG 7.7: Complex Numbers

We introduce complex numbers as a method for extend the real number square root of -1. Basic algebra is described as a continuation of techniques for radicals over the reals.

[gregbell]

Topic ideas:
1) Multiplying by i is a 2-D rotation (see Better Explained on this for an amazing treatment).
2) Multiplying by -1 is a 1-D rotation, and that's why -1 * -1 = 1
3) Are these really rotations, or is that just a useful analogy?
4) Functions, inverse functions, extraneous roots, and the problem with sqrt(x) as a function vs. using it in algebra.

These are well beneath you, but I find them interesting because they're unexpected depths on what appear to be simple topics.

[gregbell]

Thank you for the video Dr. Bob

What's the problem with having i in the denom? I stopped teaching this method of simplification years ago when calculators got capable of dividing out a complex fraction (yielding the a+bi form).

Other than tradition, and that it's sort of neat how we can make i go away, I can't figure out the value in this.

[lemyul]

No offence, you look so much older now :(