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Question
Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.
Solution
- 6 - 24i = - 6 + 24i ......(1)
(x – iy) (3 + 5i) = (3x – 5yi<sup.2 + 5xi – 3yi)
= 3x + 5y + (5x – 3y)i ......(2)
From equations (1) and (2),
3x + 5y + (5x – 3y)i = – 6 + 24i
writing real and complex numbers the same
3x + 5y = – 6 ......(3)
5x – 3y = 24 ......(4)
Equation (3) can be reduced to 3 and Equation Multiplying (4) by 5
9x + 15y = – 18 .....(5)
25x – 15y = 120 .....(6)
By adding equation (5) and equation (6),
34x = 102 या x = `102/34 = 3`
Putting the value of x in equation (3),
9+ 5y = – 6 or 5y = – 15, या y = – 3
Hence x = 3, y = – 3.
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