Complex Numbers has got to be the topic with the largest gap between how cool I think it is and how I teach it. I've struggled to teach this to kids in a way that doesn't make me nauseous, and so far I've pretty much failed. At the same time, I think that I'm making progress on sharing what I love about the topic with kids.
(I've written before about this. I ran a Global Math Department session about this.)
Here's my most recent attempt at telling a story that I like about complex numbers. I aim for practically no prerequisites, and I try to suggest problems that I think would be interesting -- for kids? -- at the bottom of each page.
I am looking for feedback. Be constructive, but tell me where I've gone wrong here. Drop a comment if you're excited. I'll be hanging out in the comments section, looking forward to some good back and forth on this.
(You might be wondering where Page 1 is. It's after Page 14, duh.)
(Also, I'm sorry that you're looking at an ad from the Scribd script. Does anyone have a pdf sharing thingy that works better than Scribd?)
(Also also, yeah, you're going to want to biggify that by clicking the bottom right corner of the Scribd widget.)
Update 7/29/13: You know, on second thought it's probably too much to assume that people will read a 17 page booklet on the internet. Maybe I'll try this post again.
Update 8/21/13: I think that a good bit of math to precede this discussion would be one that showed how certain models fail to extend to other operations.