Question

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

(a) is equal to 5/2

(b) lies in the interval (0,2)

(c) is strictly greater than 5/2

(d) is strictly greater than 3/2 but less than 5/2

Answer 1

Correct option (b) lies in the interval (0,2)

Explanation:

|z| ≥ 2 is the region on or outside circle whose centre is (0, 0) and radius is 2.

Minimum |z + 1/2| is distance of z, which lie on the circle |z| = 2 from (-1/2, 0).