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Complex Conjugation — Relative to What?

In: Clifford Algebras with Numeric and Symbolic Computations

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  • Alexander M. Soiguine

Abstract

Some initial, technically simple but fundamentally important statements concerning the very origin of the notion of a complex number are formulated in terms of the Clifford (Geometric) algebra generated by vectors in some geometrically and physically sensitive dimensions. A new insight into the sense of geometrical product is given. It is shown that it makes no sense to speak about complex numbers without identifying a corresponding two-dimensional plane. This is particularly important if the given physical situation is set in higher dimensions. Because of great importance of these questions in education and because of increasing use of graphical computer programs in mathematical education and research, some components of a computer program implementing the Geometric Algebra approach are outlined in terms of classes of the object-oriented computer language C++.

Suggested Citation

  • Alexander M. Soiguine, 1996. "Complex Conjugation — Relative to What?," Springer Books, in: Rafał Abłamowicz & Josep M. Parra & Pertti Lounesto (ed.), Clifford Algebras with Numeric and Symbolic Computations, pages 285-294, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-8157-4_19
    DOI: 10.1007/978-1-4615-8157-4_19
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