Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
0 votes

If a complex number z lies on the interior or on the boundary of a circle of radius 3 units and centre (-4,0) find the greatest and least values of $\;|z+1| \;.$

$(a)\;3 \; and\;0\qquad(b)\;6\;and\;0\qquad(c)\;4\;and\;1\qquad(d)\;5\;and\;1$

Can you answer this question?

1 Answer

0 votes
Answer : $\;6\;and\;0$
Explanation :
Distance of the point representing z from the centre of the circle is $\;|z-(-4+i0)| = |z+4|\;.$
According to given condition $\; |z+4| \leq 3$
Now $\;|z+1| = |z+4-3| \leq |z+4| + |(-3)| \leq 3+3 =6$
Therefore , the greatest value of $\;|z+1| \;$is 6
Since least value of the modulus value of a complex number is zero , the least value of $\;|z+1| =0\;.$
answered Apr 17, 2014 by yamini.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App