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 |-z|=|z| and |$z_1$ + $z_2$| $\le$ |$z_1$|+|$z_1$|

Now |z|+|z-1| = |z|+|1-z| $\ge$|z+(z-1)|=|1|=1

Hence, minimum value of |z|+|z-1| is 1.