Complex numbers product using only three multiplications

Question

We do complex number multiplication as follows:

(a + i * b) * (c + i * d) = (a * c - b * d) + i * (a * d + b * c)

The real and imaginary pa

Answer 1

For completeness, I'd like to point out Gauss' complex multiplication algorithm, which is another way to do complex multiplication with only three multiplies. To summarize, you compute

k1 = c * (a + b)
k2 = a * (d - c)
k3 = b * (c + d)
Real part = k1 - k3
Imaginary part = k1 + k2