Complex Numbers And Quadratic Equations question 132
Question: If $ z $ is a complex number, then the minimum value of $ |z|+|z-1| $ is [Roorkee 1992]
Options:
A) 1
B) 0
C) 1/2
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
First note that $ |-z|=|z| $ and $ |z_1+z_2|\le |z_1|+|z_2| $ Now $ |z|+|z-1|=|z|+|1-z|\ge |z+(1-z)|=|1|=1 $ Hence, minimum value of $ |z|+|z-1| $ is 1.
BETA
