Are complex numbers complex?

It’s an unfortunate fact of history that numbers of the form a+bi are called complex numbers. In modern English, of course, the word complex is usually associated with phrases like difficult, inscrutable, time-consuming, hard to solve, and other negative connotations that teachers would prefer to not introduce into a math class.

However, my understanding is that the other meaning of the word complex was in mind when the term complex numbers was coined. After all, in modern English, we still refer to a group of buildings as an apartment complex or maybe an office complex. In this sense, complex means two (or more) things that are joined together to form a single unit, which is precisely what happens as the real part a and the imaginary part $bi$ are joined to form a + bi. Indeed, my understanding is that complex was chosen to be the opposite of simplex, or a single unit (like a real number).

Anyway, hopefully this bit of history can make complex numbers less mystifying for students.

While I’m on the topic, the word imaginary was another unfortunate choice of words by our ancestors, but — like complex — we’re just stuck with it.

Also while I’m on the topic, this is a good chance to review a great piece of showmanship about teaching complex numbers:

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