Complex Numbers And Quadratic Equations question 684
Question: The greatest and the least value of $ |z_1+z_2| $ if $ z_1=24+7i $ and $ |z_2|=6 $ respectively are
Options:
A) $ 25,19 $
B) $ 19,25 $
C) $ -19,-25 $
D) $ -25,-19 $
Show Answer
Answer:
Correct Answer: A
Solution:
$ | z_1+z_2 |\le | z_1 |+| z_2 |=| 24+7i |+6=25+6=31 $ Also,
$ \Rightarrow | z_1+z_2 |=| z_1-(-z_2) |\ge | | z_1 |-| z_2 | | $
$ \Rightarrow | z_1+z_2 |\ge | 25-6 |=19 $ Hence the least value of $ | z_1+z_2 | $ is 19 and the greatest value is 25.
BETA
