Which values of x and y would make the following expression represent a real number?

(4 + 5i) (x + yi)

A. x = 4, y = 5

B. x = - 4, y = 0

C. x = 4, y = - 5

D. x = 0, y = 5

To make the given, (4 + 5i) (x + yi), represent a real number, multiply the first factor with its conjugate. The whole expression should also represent a difference of two squares. With this given the conjugate of the first term is 4 - 5i. Thus, the answer to this question is letter C where x is 4 and y is - 5.