question_answer

The minimum value of \[\left| z \right|+|z-i|\] is

A) 0                     

B) 1

C) 2                     

D) None of these

Correct Answer: B

Solution :

Using the result \[\left| {{z}_{1}}+{{z}_{2}} \right|\le \left| {{z}_{1}} \right|+\left| {{z}_{2}} \right|\] we get \[\left| z \right| + \left| z - i \right| = \left| z \right| + \left| i - z \right|\] [since \[\left| \,z\, \right| = \left[ -z| \right]\] \[\le \,|z+i\,-z|=\,\,\left| i \right|=1\] minimum value of \[\left| \,z\, \right| + \left| z\,-i \right|\] is 1