CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If |z1|=|z2|=|z3|=|z4|=1 and z1+z2+z3+z4=0
then least value of the expression
E=|z1z2|2+|z2z3|2+|z3z4|2+|z4z1|2 is


A

6

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

8

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

10

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

12

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B

8


E=2(|z1|2+|z2|2+|z3|2+|z4|2)
¯z1(z2+z4)¯z2(z1+z3)¯z3(z2+z4)¯z4(z1+z3)=2(|z1|2+|z2|2+|z3|2+|z4|2)
(¯z1+¯z3)(z2+z4)(¯z2+¯z4)(z1+z3)=8+|z1+z3|2+|z2+z4|28
z1+z3=(z2+z4)


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Properties of Conjugate of a Complex Number
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon