**Description**

This programme is an investigation of complex numbers. Computer animations are used to illustrate these numbers on a complex plane.

Module code and title: | M101, Mathematics: a foundation course |
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Item code: | M101; 26; 1977 |

Recording date: | 07-10-1977 |

First transmission date: | 06-08-1978 |

Published: | 1977 |

Rights Statement: | |

Restrictions on use: | |

Duration: | 00:24:30 |

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Producer: | John Jaworski |

Contributors: | Jeremy Gray; Allan I.,1936-2013 Solomon |

Publisher: | BBC Open University |

Keyword(s): | Complex numbers; Complex planes; Roots of equations; Spiral patterns |

Footage description: | Allan Solomon introduces the programme. He solves a quadratic equation and then looks at a similar equation which appears not to have roots. Jeremy Gray works out a solution for the roots of this equation, using an algebraic formula. This solution is then shown graphically by splitting the roots into two parts and plotting each on a co-ordinate, complex plane. This result shows that a quadratic equation always has two roots. The behaviour of the roots is demonstrated by a computer animation, The same technique is used to illustrate the behaviour of the roots of third and fourth degree curves. Using the complex plane, Jeremy gives examples of the addition and multiplication of complex numbers. These are illustrated with computer animations. Allan and Jeremy now look at powers of complex numbers, plotted on a complex plane. These produce a spiral, similar to those often found in nature. A shell of a sea creature, Nautilus is shown to demonstrate this relationship. Computer animations show the changing spiral pattern generated as the original complex number is shortened. A circle is generated by one complex number. On this circle are found the fifteen fifteenth roots of unity. |

Master spool number: | HOU2650 |

Production number: | 00525_4264 |

Videofinder number: | 2488 |

Available to public: | no |