The general idea of Strassens algorithm is to do fewer expensive multiplications by carefully choosing which multiplications to do and then combining them with cheaper additions / subtractions in ways so that some of the work can be reused. This problem asks you to apply the same philosophy to the (simpler) problem of multiplying two complex numbers. Let i be the square root of -1. The denition of (a+bi)(c+di) as (acbd)+(ad+bc)i leads to a brute force algorithm that does four multiplications of real numbers. You are to devise a way to multiply two complex numbers that uses only three multiplications of real numbers to compute (acbd) and (ad+bc). You can use a few extra additions and subtractions (but dont just substitute multiplication with repeated addition).