Question

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

Answer 1

- 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.