JEE Main 12 Jan 2019 Evening Question 28
Question: Let $ z _1 $ and $ z _2 $ be two complex numbers satisfying $ |z _1|=9 $ and $ |z _2-3-4i|=4 $ .Then the minimum value of $ |z _1-z _2| $ is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
Options:
A) $ \sqrt{2} $
B) 2
C) 0
D) 1
Show Answer
Answer:
Correct Answer: C
Solution:
- Given, $ |z _1|=9, $ represents a circle with centre $ C _1(0,0) $ and radius $ r _1=9 $ .
Also, $ |z _2-(3+4i)|=4 $ represents a circle with centre $ C _2(3,4) $ and radius $ r _2=4. $
$ \therefore $ $ C _1C _2=|r _1-r _2|=5 $
So, circles touches each other internally.
$ \therefore $ $ |z _1-z _2{| _{\min }}=0 $
