Question

If (1 + i)(z + $\overline{z}$) - i(a + i)(z - $\overline{z}$) + 2(a - 1)i = 0 and z$\overline{z}$ = 5 then the value of 'a' is

• A.
• B.
• C.
• D. 0

Answer 1

The correct option is A

Put z = x + iy then z + $\overline{z}$ = 2x and z - $\overline{z}$ = 2iy

(1 + i)(z + $\overline{z}$) - i(a + i)(z - $\overline{z}$) + 2(a - 1)i = 0

After simplification of equation (i), we get

x = -a, y = 1

Using in (ii) $\Rightarrow$ $a^2$ + 1 = 5 $\Rightarrow$ a = $\pm$2