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This programme is an investigation of complex numbers. Computer animations are used to illustrate these numbers on a complex plane.
Metadata describing this Open University video programme
Module code and title: M101, Mathematics: a foundation course
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