If z is complex number such that | z | \geq 2, then the minimum value of \left|\right. \textrm{ } z + \frac{1}{2} \textrm{ } \left|\right.

Engineering

Mathematics

Geometry of Complex Number

Question

If z is complex number such that | z | $\geq$ 2, then the minimum value of $| z + \frac{1}{2} |$

lies in the interval (1, 2)

is strictly greater than

is equal to

is strictly greater than $\frac{3}{2}$ but less than

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$| z - (\frac{- 1}{2}) |$

= distance of z from point $(\frac{- 1}{2})$

= $\frac{3}{2}$ is its minimum value and it goes to infinity