# For any complex number z,the minimum value of $\mid z\mid+\mid z-2i\mid$ is

$\begin{array}{1 1}(A)\;1&(B)\;2\\(C)\;0&(D)\;\text{None of these}\end{array}$

## 1 Answer

For $z\in C$
$\mid 2i\mid=\mid z+(2i-z)\mid\leq |z|+|2i-z|$
$\Rightarrow 2\leq |z|+|z-2i|$
$\Rightarrow$ Minimum value of $\mid z\mid+\mid z-2i\mid$ is 2 which is attained when $z=i$
Hence (B) is the correct answer.
answered Apr 10, 2014

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