Which of the following of x and y would make up the following expression represent a real number? (4+5i) (x+yi)

x = 4 and y = - 5

Step-by-step explanation:

note that the product of a complex number and it's conjugate is real

That is

(a + bi) (a - bi) where a, b are real

= a² - abi + abi - b²i²

= a² + b² ← a real number

For (4 + 5i) (x + yi) to be real

we require (x + yi) to be the conjugate of 4 + 5i, that is 4 - 5i

(4 + 5i) (4 - 5i) ⇒ x = 4 and y = - 5