JEE Main & Advanced
Mathematics
Complex Numbers and Quadratic Equations
Question Bank
Self Evaluation Test - Complex Numbers and Quadratic Equations
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