Geometric Multiplication of Vectors pp 161-188 | Cite as

# Appendix

Chapter

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## Abstract

The exponential function can be defined by the series expansionwhere it is important to note that for a definite magnitude |*x*| we have convergence. Therefore, we can define the exponential function of the elements of a geometric algebra. In *Cl*3, we have four important types of elements (numbers): *nilpotents* (dual numbers, square to zero), *imaginary* (square to −1), *hyperimaginary* (square to 1), and *idempotents* (square to itself). Nilpotents are the easiest to deal with: the expansion (∗) gives zeros, except for the first two terms, and consequently, we have

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