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Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.

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Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.
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Equating real and imaginary parts, we obtain

Multiplying equation (i) by 3 and equation (ii) by 5 and then adding them, we obtain

Putting the value of x in equation (i), we obtain

Thus, the values of x and y are 3 and –3 respectively.

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