Cohl Furey sounds like a goddamn new Marvel character, but actually she's a mathematical physicist. Can that really be her name? As a novelist, I feel reality is cheating by being so fucking dramatic:https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/ …
So with 'i' the process goes, informally, something like... ok we still have all the real numbers like 3 and pi. 'let a be a real number' Multiplication means we have stuff like 12i and -i/4. 'bi, where b is a real number' Addition means we have pairs like 3 + 12i and pi - i/4.
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So we at least have to handle everything that looks like 'a + bi, where a and b are real numbers' It turns out that this is all you need -- you can add, subtract, multiply and divide these guys and you don't get anything hairier than 'a + bi'.
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It takes some checking -- proving division works is a bit of a slog. But this is the kind of thing we algebraists do for a living.
End of conversation
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.