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

We know that, $|-z|=|z|$ and Now,

$\left|z_1+z_2\right|  \leq\left|z_1\right|+\left|z_2\right| $

$ |z|+|z-1| =|z|+|1-z| $

$ \geq|z+(1-z)|=|1|=1 $

$ |z|+|z-1|  \geq 1$

So, The correct option will be (A).