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13 June, 13:47

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

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  1. 13 June, 14:16
    0
    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
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