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    • Solution to Puzzle No. 5 - complex multiplication

      1 September, 1998
      September 1998

      For the question see "Puzzle No. 5 - complex multiplication" in issue 5.

      We can calculate p and q using just three multiplications:-

      q=ad+bc

      the three products used being

      In fact this is not the only way to calculate p and q using three multiplications. There are many variations on the above idea, but all of them are essentially the same. If you struggled to get the solution to this issue's puzzle, why not have a go at experimenting to see how many ways you can calculate p and q using just three multiplications.

      The time taken to multiply n by another number m of similar size is roughly proportional to (log n)2, whereas the time taken to add n to m is about log n. Hence the above procedure can save a lot of computational time in any program that has to perform many complex multiplications. A good example would be the programs used to generate fractal images.

      To find out more about fractals, why not see "Modelling nature with fractals", and " The origins of fractals" elsewhere in this Issue.

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      Anonymous

      2 August 2012

      Permalink
      Comment

      I think the correct formula for q should be
      q = ad + bc

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      Marianne

      8 August 2012

      In reply to Mistake in formula by Anonymous

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      Comment

      Yes, you're right, thanks for picking that up! We've corrected the mistake.

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