• # question_answer If $z$ is a complex number, then the minimum value of $|z|+|z-1|$ is [Roorkee 1992] A) 1 B) 0 C) 1/2 D) None of these

First note that $|-z|\,=\,|z|$ and $|{{z}_{1}}+{{z}_{2}}|\,\le \,|{{z}_{1}}|+|{{z}_{2}}|$ Now $|z|+|z-1|\,=\,|z|+|1-z|\,\ge \,|z+(1-z)|\,=\,|1|=1$ Hence, minimum value of$|z|+|z-1|$is 1.