Question

If the complex number z satisfy the equation (i – z) (1 + 2i)

+ (1 – iz) (3 – 4i) = 1 + 7i, then z + $\bar{z}$ + z$\bar{z}$is equal to –

• A. 0
• B. 1
• C. –1
• D. None of these

Answer 1

Answer: (A)

0

Answer 2

Sol. (i – z) (1 + 2i) + (1 – iz) (3 – 4i) = 1 + 7i

Ž i – z – 2 – 2iz + 3 – 3iz – 4i – 4z = 1 + 7i

Ž z + iz + 2 = 0

Ž (x – y + 2) + i (x + y) = 0 [put z = x + iy]

Ž x – y + 2 = 0 and x + y = 0 Ž x = –1, y = 1

\ z = –1 + i \ z +$\bar{z}$ + z$\bar{z}$ = –2 + 2 = 0.