Complex Numbers And Quadratic Equations question 624
Question: The greatest and the least absolute value of $ z+1, $ where $ |z+4|\le 3 $ are respectively
Options:
A) 6 and 0
B) 10 and 6
C) 4 and 3
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
We have $ |z+1|=|z+4-3| $ …(i) Now $ |z+4-3|\le |z+4|+|-3|\le 3+3=6 $ [Given $ |z+4|\le 3 $ & $ |-3|=3 $ ]
$ \therefore |z+1|\le 6 $ Again $ |z+1|\ge 0 $ [modulus is always non- negative]
$ \therefore $ Least value of $ |z+1| $ maybe zero, which occurs when $ z=-1, $ For $ z=-1, $ $ |z+4|=|-1+4|=3 $ Which satisfies the given condition that $ |z+4|\ge 3 $ Hence, the least and the greatest values of $ |z+1| $ are 0 and 6
BETA
