Question

If complex no. z and its conjugate $\bar{z}$satisfy z$\bar{z}$ + 2i (z + $\bar{z}$) = 12 + 8i then value of z is

• A. 2$\sqrt{2}$± 2i
• B. 2± 2$\sqrt{2}$i
• C. 2 ±$\sqrt{2}$i
• D. None

Answer 1

Answer: (B)

2± 2$\sqrt{2}$i

Answer 2

Sol. Let z = x + iy

Q z$\bar{z}$+ 2i (z + $\bar{z}$) = 12 + 8i

|z|² + 4i Re(z) = 12 + 8i

\ |z|² = 12, 4 Re(z) = 8

x² + y² = 12, Re(z) = 2

, x = 2

\ y = ± 2$\sqrt{2}$

So z = 2 ± i2$\sqrt{2}$