Question

 If z is a complex number, then the minimum value of |z| + |z − 1| is ______.

Answer 1

First, note that |-z|=|z| and |z1 + z2| ≤ |z1| + |z2|
Now |z| + |z-1| = |z| + |1 - z| ≤ |z + (1 - z)|

= |1|

= 1

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