creating complex analysis in abstract space

we know that in complex analysis i*i = -1 now lets suppose that we have a space (A) and j belong to A. suppose that j*j = -i where i is a unique square matris in A. now the task is that: create the space A and do all operations wich was done in complex numbers space (C)

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Originally Posted by hers19

we know that in complex analysis i*i = -1 now lets suppose that we have a space (A) and j belong to A. suppose that j*j = -i where i is a unique square matris in A. now the task is that: create the space A and do all operations wich was done in complex numbers space (C)

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What kind of space is this? Vector space?

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Originally Posted by Drexel28

What kind of space is this? Vector space?

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elements of A are square matrises (n*n, n belongs N). and the task is to create complex analysis in this Space.( for example the complex space (C) that we know may be created as follows : first we suppose i*i = -1 (i belongs C) and each element of C can be indicated x+i*y then we define complex numbers sequences, limit, then complex functions, diferentiation ,integration and so on )