> My 11-year-old son managed, without knowing algebra, to find the square root of i without guidance.

I'm curious what this means. To my mind, "without guidance" and also without knowing algebra, he wouldn't know what i was, and would therefore be unable to do any computation with it.

He knew that i was the square root of 1 and he had learned some really basic skills like the distributive law, so he managed to work out that (a+bi)(a+bi) = a²-b²+2abi, but it was entirely self-directed on his part. I had taught him some how to solve simple linear equations but he didn’t have the skills to be able to work out that he needed a=b and 2ab=1 so there were some trial and error attempts at finding values that worked.

(I did the same thing as he did, but in high school sophomore year while bored in health class and with a bit more sophistication mathematically than what he had.)