wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let C1 and C2 are concentric circles of radius 1 unit and 8/3 unit , respectively, having centre at (3,0) on the Argand plane. If the complex number z satisfies the inequality
log1/3(|z3|2+211|z3|2)>1 then

A
z lies outside C1 but inside C2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
z lies inside C1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
z lies outside C2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
none of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A z lies outside C1 but inside C2
log1/3(|z3|2+211|z3|2)>1
Let |z3|=tt>0
for function to be defined
t2+211t2>0
t>211(1)

log1/3(|z3|2+211|z3|2)>1
t2+211t2<13
3t211t+83(11t2)<0
(3t8)(t1)11t2<0
t(1,83)(2) [using (1)]
Hence
1<t<83
1<|z3|<83
z lies outside C1 but inside C2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
This Is an Interesting Sum Part 1
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon