Show how to multiply the complex numbers $a + bi$ and $c + di$ using only three multiplications of real numbers. The algorithm should take $a$, $b$, $c$, and $d$ as input and produce the real component $ac - bd$ and the imaginary component $ad + bc$ separately.

Calculate the following products: $ac$, $bd$, and $(a + b)(c + d)$.
Hence, the real component = $ac - bd$ and the imaginary component = $(a + b)(c + d) - ac - bd = ad + bc$ which we got by using only additions/subtractions.