If (1 + i)z = (1 – i)(\bar{z}), then z is – | MATH - CONJUGATE, MODULUS AND ARGUMENT OF COMPLEX NUMBERS | SolveeIt | Solveeit

Today, August 18

Question

If (1 + i)z = (1 – i) $\bar{z}$ , then z is –

A

x(1 – i), x Ī R

B

x (1 + i), x Ī R

C

$\frac{x}{1 + i}$ , x Ī R⁺

D

None of these

Answer

x(1 – i), x Ī R

Explanation

Solution

Sol. (1 + i)(x + iy) = (1 – i)(x – iy)

(x – y) + i(x + y) = (x – y) – i(x + y)

\ x + y = 0

\ z = x – ix = x(1 – i)