question_answer

If z is a complex number, then the minimum value of \[\left| z \right|+\left| z-1 \right|\] is-

A) 1                     

B)        0

C) 1/2                   

D)        None of these

Correct Answer: A

Solution :

[a] \[{{\left[ \left| \underset{p}{\mathop{Z}}\,-\underset{A}{\mathop{0}}\, \right|-\left| \underset{p}{\mathop{Z}}\,-\underset{B}{\mathop{1}}\, \right| \right]}_{\min }}\] \[\Rightarrow {{\left( PA+PB \right)}_{min}}=?\]                      \[\downarrow \] it is only possible when p lies between A and B. \[\Rightarrow {{\left( PA+PB \right)}_{min}}=AB=1\]