For any complex number z,  the minimum value of |z|+|z−2i|  is

We have, for z∈C         |2 i|=|z+(2i−z)|≤  |z|+|2i−z|        since z1+z2≤z1+z2⇒        2≤|z|+|z−2i|Thus, minimum value of |z|+|z−2i|  is 2 and it is attained for any z  lying on the segment joining z=0  and z=2i.