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Math Help - Complex numbers

  1. #1
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    Complex numbers

    A complex number a + bi, where i = \sqrt[root]{-1}, can be represented by the pair (a,b). How could you use only three real number multiplications to obtain (e,f), the product of a + bi and c + di?
    Last edited by vexiked; February 7th 2010 at 07:56 PM.
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  2. #2
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    Quote Originally Posted by vexiked View Post
    A complex number a + bi, where i = \sqrt[root]{-1}, can be represented by the pair (a,b). How could you use only three real number multiplications to obtain (e,f), the product of a + bi and c + di?
    Form these products: (1) ac; (2) bd; (3) (a+b)(c+d). Then e = (1) (2), f = (3) (1) (2). (I'm assuming that addition and subtraction are meant to be "cost-free", and it's only the number of multiplications that has to be minimised.)
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  3. #3
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    Yeah addition and subtraction are cost free.. Thanks!
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