If z is a complex number such that z ≥ 2 , then the minimum value of z + 1 2 :

Step-by-step solution

z ≥ 2     i . e .,   z - 0 ≥ 2 ∴ The distance of ' z ' from origin is greater than two. We have to find minimum of z + 1 2 z + 1 2 = z - - 1 2 = distance of z from - 1 2 ,   0 . On the argand plane, z lies in the dotted regions I ,   II ,   III ,   IV . ∴ The minimum distance is from the point B = 2 - 1 2 = 3 2 ⇒ 3 2 ∈ 1 ,   2