If `z` is a complex number such that `|z|>=2` then the minimum value of `|z+1/2|` is

Options

A. is equal to 5/2
B. lies in the iterval (1,2)
C. is strictly greater than 5/2
D. is strictly greater than 3/2 but less than 5/2

Answer

B

Explanation

`|z| ge 2` is the region on or outside ciecle whose centre is (0,0) and radius is 2.
Minimum `|z+1/2|` is distance of z, which the on circle |z| = 2 from (-1/2,0)
`therefore " Minimum " |z+1/2|`=Distance of `(-1/2,0)` from (-2,0)
`rArr sqrt((-2+1/2)^2)+0=3/2=sqrt((-1/2+2)^2+0)=3/2`

Geometrically Min `|z+1/2|=AD`
Hence ,minimum value of `|z+1/2|` lies in the interval (1,2)