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Division in a binary representation for complex numbers

Citation

Blest, DC and Jamil, T, Division in a binary representation for complex numbers, International Journal of Mathematical Education in Science and Technology, 34, (4) pp. 561-574. ISSN 0020-739X (2003) [Refereed Article]

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The definitive published version is available online at: http://www.tandf.co.uk/journals

DOI: doi:10.1080/0020739031000108592

Abstract

Computer operations involving complex numbers, essential in such applications as Fourier transforms or image processing, are normally performed in a 'divide-and-conquer' approach dealing separately with real and imaginary parts. A number of proposals have treated complex numbers as a single unit but all have foundered on the problem of the division process without which it is impossible to carry out all but the most basic arithmetic. This paper resurrects an early proposal to express complex numbers in a single 'binary' representation, reviews basic complex arithmetic and is able to provide a fail-safe procedure for obtaining the quotient of two complex numbers expressed in the representation. Thus, while an outstanding problem is solved, recourse is made only to readily accessible methods. A variety of extensions to the work requiring similar basic techniques are also identified. An interesting side-line is the occurrence of fractal structures, and the power of the 'binary' representation in analysing the structure is briefly discussed.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Pure Mathematics
Research Field:Algebra and Number Theory
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Blest, DC (Associate Professor David Blest)
ID Code:29131
Year Published:2003
Deposited By:Mathematics
Deposited On:2003-08-01
Last Modified:2010-05-03
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