Find the real values of x and y for which:(1 – i) x + (1 + i) y = 1

1.	Find the real values of x and y for which:(1 – i) x + (1 + i) y = 1 – 3i
Answer» (1 – i) x + (1 + i) y = 1 – 3i ⇒ x – ix + y + iy = 1 – 3i ⇒ (x + y) – i(x – y) = 1 – 3i Comparing the real parts, we get x + y = 1 …(i) Comparing the imaginary parts, we get x – y = -3 …(ii) Solving eq. (i) and (ii) to find the value of x and y Adding eq. (i) and (ii), we get x + y + x – y = 1 + (-3) ⇒ 2x = 1 – 3 ⇒ 2x = -2 ⇒ x = -1 Putting the value of x = -1 in eq. (i), we get (-1) + y = 1 ⇒ y = 1 + 1 ⇒ y = 2

Find the real values of x and y for which:(1 – i) x + (1 + i) y = 1 – 3i

Answer»

(1 – i) x + (1 + i) y = 1 – 3i

⇒ x – ix + y + iy = 1 – 3i

⇒ (x + y) – i(x – y) = 1 – 3i

Comparing the real parts, we get

x + y = 1 …(i)

Comparing the imaginary parts, we get

x – y = -3 …(ii)

Solving eq. (i) and (ii) to find the value of x and y

Adding eq. (i) and (ii), we get

x + y + x – y = 1 + (-3)

⇒ 2x = 1 – 3

⇒ 2x = -2

⇒ x = -1

Putting the value of x = -1 in eq. (i), we get

(-1) + y = 1

⇒ y = 1 + 1

⇒ y = 2