One of my little obsessions is teaching complex numbers, but it’s really hard to find genuine instances of complex number mistakes. You start looking around at the most pernicious complex number mistakes, and they’re a lot like this one here: essentially algebraic. These mistakes, to my mind, are indistinguishable from the sorts of mistakes you’d expect from $(4-6x)^2.$

That observation is probably helpful in itself, though. The mistakes that we see from kids working with complex numbers are essentially algebraic mistakes. That means that kids aren’t really seeing much of a difference between the algebra that they’re usually asked to do and their work with complex numbers. Complex number arithmetic is just algebra with a twist.

• Michael Paul Goldenberg

Couple of comments: 1) What are you hoping they’ll get out of this work? That is, are you looking to go into complex variables with them – vector and trig interpretations, etc., roots of unity, and so forth, applications, or what? 2) What other sorts of mistakes might crop up if this is strictly the usual quick-hit high school excursion into complex number arithmetic – adding, multiplying, powers, etc.? 3) Have you by any chance bumped into the geometric interpretation in two-space of the roots of quadratic equations? If not, I just did very recently and I think it’s very cool: http://www.math.hmc.edu/funfacts/ffiles/10005.1.shtml

• BillyeHaber3

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