(9am to 6pm)

Ask Questions, Get Answers

Want help in doing your homework? We will solve it for you. Click to know more.

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

Need homework help? Click here.
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 by sreemathi.v

Related questions