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filter54321

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**Are there "imaginary" numbers other than i?**

I'm taking a class in complex analysis and the professor wrote the textbook so I'm getting most of it. There is one elephant in the room though, and I haven't been able to make office hours to clear it up.

Are there "imaginary" numbers other than I. We declared that i existed because it was useful (as we constructed negative numbers in real analysis because they were useful). We did some proofs to show that algebra would still work, then we constructed C using the real line and complex numbers of the form a+bi.

While jumping right to C will let you play with functions of complex numbers, the professor never really addressed if there are other "fake" numbers. Is there for example, a j=1/0 or other nonsense that adds dimensions to C? Could you then compute with something like a+bi+cj? If utility and computability is the standard for creating a number, it would reasonable that there should be other "complex families" of them out there.