In mathematics, the multicomplex number are defined inductively as follows: Let C0 be the real number system. For every let in be a square root of−1, that is, an imaginary unit (commutativity is the complex number is the bicomplex number is the tricomplex number system of Corrado Segre is the multicomplex number system of order n.

forms a Banach algebra. G. Bayley Price

The multicomplex number systems are not to be confused with Clifford numbers (elements of a Clifford algebra), since Clifford's square roots of when for Clifford).

Because the multicomplex numbers have several square roots of –1 that commute, they also have zero divisors of the split-complex numbers, and therefore the multicomplex numbers contain a number of copies of the split-complex number plane.

With respect to subalgebra, k = 0, 1, ..., is of dimension

References

• G. Baley Price (1991) An Introduction to Multicomplex Spaces and Functions, Marcel Dekker.

• Corrado Segre (1892) "The real representation of complex elements and hyperalgebraic entities" (Italian), Mathematische Annalen 40:41367 (see especially pages 45567).