Question

Find the values of x and y which satisfy the following equations (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 real and imaginary parts, we get

x + 2y = 5 ……(i)

and 2x – 3y = -4 …..(ii)

Equation (i) x 2 – equation (ii) gives

7y = 14

∴ y = 2

Substituting y = 2 in (i), we get

x + 2(2) = 5

x + 4 = 5

∴ x = 1

∴ x = 1 and y = 2

Check:

For x = 1 and y = 2

Consider, L.H.S. = (x + 2y) + (2x – 3y)i + 4i

= (1 + 4) + (2 – 6)i + 4i

= 5 – 4i + 4i

= 5

= R.H.S.