My older son moved on to a new chapter in his algebra book today – complex numbers. We’ve done work with complex numbers before, and even by coincidence this weekend in our Mandelbrot set projects:
My son chose an interesting problem about simplifying complex numbers for our video today. The problem ask you to simplify the expression (5 + 3i) / (3 – 4i).
I was pleasantly surprised by his approach to the problem:
We had not discussed any of the problems or examples in the section, so it probably isn’t much of a surprise that my guess about the approach he would take to the problem was wrong. I thought it would be useful to show him what an approach similar to “rationalizing the denominator” would look like:
I love how different these two approaches look at first glance. In fact, it is pretty surprising that you arrive at the same answer. Feels like this would be a fun example to introduce matrix inversion.