Extension of Complex Numbers [closed]

complex-numbers number-systems

Does there exist a number system that contains $\mathbb C$? If so, how many such systems are there? Why are they developed? Which are the larger ones?


Well, you could extend the complex number system to the bigger one, say the Quaternions, Octonions, etc. However, one should note that for what reason are we trying to extend a particular system. If you want to solve polynomial equation over C, this is complete in itself. C is an algebraically closed field, i.e. polynomials over C has a root in C. So any algebraic extension is just C itself.

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