The number i has its “roots” in the work of early Arabic mathematicians, the same people who first really understood the number. But they weren’t quite as good with i as they were with 0; they didn’t really get it. They had some concept of the roots of a cubic equation, where sometimes the tricks for finding the roots just didn’t work. They knew there was something going on, some way that the equation needed to have roots, but just what that really meant, they didn’t get.

Things stayed that way for quite a while. Mathematicians studying algebra knew that there was something missing in a variety of mathematical concepts, but no one understood how to solve the problem. What we know as algebra developed for many years, and various ...

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