Multicomplexe number

In Mathematical, the numbers multicomplexe S form a commutative algebra with N dimensions generated by an element E which satisfies $~e^n\; =\; -1\; \backslash ,$. A number multicomplexe X can be written in the form

$x\; =\; \backslash \; sum\_\; \{I\; =\; 0\}\; ^\; \{n-1\}\; x\_i\; e^i\; \backslash ,$

with $~e^n\; =\; -1\; \backslash ,$ and $~x\_i\; \backslash ,$ real. It is possible to write any number multicomplexe X (with $||\; X\; ||\; \backslash \; 0\; \backslash ,$) in the form of an exponential representation

$x\; =\; \backslash \; sum\_\; \{i=0\}\; ^\; \{n-1\}\; x\_i\; e^i\; =\; \backslash \; rho\; \backslash \; exp\; (\backslash \; sum\_\; \{i=1\}\; ^\; \{n-1\}\; \backslash \; Theta\; \{\}\; \_i\; e^i)$.

A particular case of the multicomplexes numbers are the numbers bicomplexes.

References

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

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