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If z is a complex number such that |z|>=...

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

A

is equal to `(5)/(2)`

B

lies in the interval (1,2)

C

is strictly gerater than `(5)/(2)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
`|z| ge2`
`therefore |z+(1)/(2)||ge|-|(1)/(2)||ge |2-(1)/(2)|ge(3)/(2)`
Hence, minimun distance between z and `(-(1)/(2),0)` is `(3)/(2)`.
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