Question

Find the values of x and y which satisfy the following equations (x, y ∈ R),

If x(1 + 3i) + y(2 – i) – 5 + i³= 0, find x + y

Answer 1

x(1 + 3i) + y(2 – i) – 5 + i³ = 0

x + 3xi + 2y – yi – 5 – i = 0 ……[∵ i³ = -i]

(x + 2y – 5) + (3x – y – 1)i = 0 + 0i

Equating real and imaginary parts, we get

x + 2y – 5 = 0 …..(i)

and 3x – y – 1 = 0 ……(ii)

Equation (i) + equation (ii) × 2 gives

7x – 7 = 0

7x = 1

∴ x = 1

Substituting x = 1 in (i), we get

1 + 2y – 5 = 0

2y = 4

y = 2

∴ x = 1 and y = 2

∴ x + y = 1 + 2 = 3