Question

Solve the following equation for x, y ∈ R:

(4 – 5i) x + (2 + 3i) y = 10 – 7i

Answer 1

(4 – 5i) x + (2 + 3i) y = 10 – 7i
∴ (4x + 2y) + (3y - 5x) i = 10 – 7i
Equating real and imaginary parts, we get
4x + 2y = 10
i.e., 2x + y = 5         ...(i)
and 3y – 5x = – 7   ...(ii)
Equation (i) x 3 – equation (ii) gives
11x = 22
∴ x = 2
Putting x = 2 in (i), we get
2(2) + y = 5
∴ y = 1
∴ x = 2 and y = 1.