Question

If z is a complex number , then the minimum value of $|z|+|z-1|$ is

• A. 1
• B. $0$
• C. 1/2
• D. None of these

Answer 1

The correct option is A 1

First note that $\mid -z\mid =\mid z\mid$ and $\mid z_1+z_2\mid \le \mid z_1\mid +\mid z_2\mid$
Now $\mid z\mid +\mid z-1\mid =\mid z\mid +\mid 1-z\mid \ge \mid z+(1-z)\mid =\mid 1\mid =1$
Hence,minimum value of $\mid z\mid +\mid z-1\mid$ is 1