Show how to multiply the complex numbers and using only three multiplications of real numbers. The algorithm should take , , , and as input and produce the real component and the imaginary component separately.

I think there is no “methodical” way to show this except for manipulating the variables. If there is, please leave a comment - I’ll add it here.

Calculate the following products: , , and .

Hence, the real component = and the imaginary component = which we got by using only additions/subtractions.

If you have any question or suggestion or you have found any error in this solution, please leave a comment below.