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