Answer :

Let us assume, z = (x – iy) (3 + 5i)

z = 3x + 5xi – 3yi – 5yi2


= 2x + 5xi – 3yi + 5y


= (3x + 5y) + i (5x – 3y)


= (3x + 5y) – i (5x – 3y)


It is given in the question that, = - 6 – 24i


Now by equating the real and imaginary parts of the equation, we get:


3x + 5y = - 6 (i)


5x – 3y = 24 (ii)


Now, by multiply equation (i) by 3 and equation (ii) by 5 and then by adding them both we get:


34x = 102



= 3


Now putting the value of x in (i), we get:


3 × 3 + 5y = - 6


5y = - 15



Hence, x = 3 and y = - 3


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