My younger son has been learning about complex numbers in Art of Problem Solving’s Precalculus book lately, and today I thought it would be fun for him to see a little bit about what complex functions “look” like.

We started with a quick review of what he knows about complex numbers and then we talked a bit about why graphing a function of a complex variable is difficult:

Next we talked about graphing a specific function ->

Now we moved to Juan Carlos’s plotter. Here we discussed and then where varies between -1 and 1.

We had a couple of slips of the hand trying to type in between the tripod in this and the next video – that’s why you’ll see a few jumps in the vids.

Finally, we wrapped up by having my son graph a few functions that he created. It was fun to see what he thought about those functions: