Which values of x and y would make the following expression represent a real number? open paren 4 plus 5 i close paren times open paren x plus y i close paren

Multiply the factors: (4 + 5i)(x + yi) = (4x − 5y) + (4y + 5x)i. For the product to be real, its imaginary part must be zero, so 4y + 5x = 0. With x = 4 and y = −5, this becomes 4(−5) + 5(4) = 0, so choice C, x = 4 and y = −5, makes the expression real.

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