Question

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

• A. 1
• B. 2
• C. 3
• D. none of these

Answer 1

The correct option is B 2

$\mid z_1-z_2\mid \le \mid z_1\mid +\mid z_2\mid$
Solution: $\mid z-(z-2)\mid \le \mid z\mid +\mid z-2\mid$
$\mid z-(z-2)\mid \le \mid z\mid +\mid z-2\mid$
$2\le \mid z\mid +\mid z-2\mid$
Minimum value of $\mid z\mid +\mid z-2\mid$ is 2