Correct option (A) 1 < Re(z) ≤ 2√3 and |Im(z)| < 2√2
Let z = x + iy
Therefore, according to given inequations, we have
5 < x2 + y2 ≤ 12
So, it represents the region bounded in between two concentric circles centred at origin of radii √5 and 2√3 units.
and (z - z)2 + 8(z + z) > 0
⇒ (2y/i)2 + 8(2x) > 0
⇒ -4y2 + 16x > 0 ⇒ y2 < 4x
represents the region inside the parabola y2 = 4x. The common region bounded is shown in Fig.
The point of intersections are
x2 + y2 = 5 and y2 = 4x
⇒ x2 + 4x - 5 = 0
⇒ x = 1, - 5 x2 + y2 = 12 and y2 = 4x
⇒ x2 + 4x - 12 = 0