Question

Question 14 Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.

Class X1 - Maths -Complex Numbers and Quadratic Equations Page 113

Answer 1

(x - iy)(3 + 5i) is the conjugate of ( -6 -24i)
Let z = (x - iy)(3 + 5i)
= x(3 + 5i) -iy(3 + 5i)
= 3x + 5xi - 3yi -5yi²
= (3x + 5y) + (5x - 3y)i
now, conjugate of z = (3x + 5y) -(5x -3y)i = -6 -24i
Compare both sides,

(3x + 5y) = -6 -----(1)
(5x -3y) = 24 ----(2)
solve both equations,
Do eqn (1) × 3 +eqn (2) × 5

9x + 25x = -18 +120
34x = 102
x = 3 and y = -3