A complex number a + bi, where i = , 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.)