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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]
Copyright StatementThe definitive published version is available online at: http://www.tandf.co.uk/journals DOI: doi:10.1080/0020739031000108592 AbstractComputer 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.
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