question_answer

If z is a complex number such that\[|z|\ge 2,\]then the minimum value of \[\left| z+\frac{1}{2} \right|:\]   JEE Main  Solved  Paper-2014

A) is equal to \[\frac{5}{2}\]

B) lies in the interval (1, 2)

C) is strictly greater than \[\frac{5}{2}\]

D) is strictly greater than \[\frac{3}{2}\]but less than \[\frac{5}{2}\]

Correct Answer: B

Solution :

\[\left| z+\frac{1}{2} \right|=\left| z-\left( -\frac{1}{2} \right) \right|\]The minimum value of\[\left| z+\frac{1}{2} \right|\]is\[\frac{3}{2}\]