Multicomplex number

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In mathematics, the multicomplex numbers form a commutative n dimensional algebra generated by one element e which satisfies ~e^n = -1. A multicomplex number x can be written as

x = \sum_{i = 0}^{n-1} x_i e^i

with ~e^n = -1 and ~x_i real. It is possible to write any multicomplex number x (with || x || \ne 0) in an exponential representation

x = \sum_{i=0}^{n-1} x_i e^i = \rho \exp ( \sum_{i=1}^{n-1} \Theta{}_i e^i ).

A special case of multicomplex numbers are the bicomplex numbers.

[edit] References

  • G. Baley Price, An Introduction to Multicomplex Spaces and Functions, Marcel Dekker Inc., New York, 1991
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