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.