Question

Find the values of the real numbers x and y, if the complex numbers

(3 – i)x – (2 – i)y + 2i + 5 and 2x + (– 1 + 2i)y + 3 + 2i are equal

Answer 1

(3 – i)x – (2 – i)y + 2i + 5 = 2x + (– 1 + 2i)y + 3 + 2i

⇒ 3x – ix – 2y + iy + 2i + 5 = 2x – y + 2yi + 3 + 2i

⇒ (3x – 2y + 5) + 1(– x + y + 2) = (2x – y + 3) + i(2y + 2)

Equate real parts on both sides

3x – 2y + 5 = 2x – y + 3

x – y = – 2   ........(1)

Equate imaginary parts on both sides

– x + y + 2 = 2y + 2

– x – y = 0

x + y = 0  ........(2)

(1) + (2)

⇒ 2x = – 2

x = – 1

Substituting x = – 1 in (2)

– 1 + y = 0

⇒ y = 1

∴ x = – 1, y = 1