### 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.

Original language | English |
---|---|

Pages (from-to) | 561-574 |

Number of pages | 14 |

Journal | International Journal of Mathematical Education in Science and Technology |

Volume | 34 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2003 |

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### ASJC Scopus subject areas

- Mathematics (miscellaneous)
- Education
- Applied Mathematics

### Cite this

**Division in a binary representation for complex numbers.** / Blest, David C.; Jamil, Tariq.

Research output: Contribution to journal › Article

*International Journal of Mathematical Education in Science and Technology*, vol. 34, no. 4, pp. 561-574. https://doi.org/10.1080/0020739031000108592

}

TY - JOUR

T1 - Division in a binary representation for complex numbers

AU - Blest, David C.

AU - Jamil, Tariq

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

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U2 - 10.1080/0020739031000108592

DO - 10.1080/0020739031000108592

M3 - Article

VL - 34

SP - 561

EP - 574

JO - International Journal of Mathematical Education in Science and Technology

JF - International Journal of Mathematical Education in Science and Technology

SN - 0020-739X

IS - 4

ER -