I showed the students complex numbers today, in the context of solving the damped harmonic oscillator. I took my time, and treated it as a cultural romp rather than a physics problem, so I enjoyed myself. What I was surprised to learn is that almost every student in the room knew that the square root of negative one is i. What is up with high school math that every student in the room learned what an imaginary number is, while not a single one learned how to program a computer? Which is easier, which is more relevant to them, and which is more natural given their interests and materials? I would say: Programming, programming, and programming!
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