Question

Find the value of x and y which satisfy the following equation (x, y∈R).

(x + 2y) + (2x − 3y)i + 4i = 5

Answer 1

(x + 2y) + (2x − 3y)i + 4i = 5

∴ (x + 2y) + (2x − 3y)i = 5 − 4i

Equating the real and imaginary parts separately, we get,

x + 2y = 5     ....(1)

and 2x − 3y = − 4   ...(2)

Multiplying equation (1) by 2, we get,

2x + 4y = 10

Subtracting equation (2) from this equation, we get,

7y = 14

∴ y = 2

Substituting y = 2 in (1), we get,

x + 2(2) = 5

∴ x + 4 = 5

∴ x = 1

Hence, x = 1 and y = 2.