My question would be very short. As we all know, there are complex, quaternion number systems, which are based on multiplication and roots. So, my question is... Is there any other complex number systems that are NOT based on number roots? For example, to assume that sin(x) = 2 has some solution, it is not something different than imaginary (complex) number, because circle's equation shows it. So, does other complex number systems exist?
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What do you mean by "number system"? You might find Cayley-Dickson construction interesting. – Marcin Łoś Jun 21 '14 at 07:53
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Oh it really seems mistaken, it should be just "system". – Martynas Riauka Jun 21 '14 at 07:57
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By the way, Cayley-Dickson construction is familiar for me and it is not exactly fit with my topic. – Martynas Riauka Jun 21 '14 at 07:59