Multicomplex number

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 $||x||\neq 0$) 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 (if we take the coefficients, $x_{0}$ through $x_{n-1}$, to be complex, and n = 2).

References

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