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

If z1+z2+z3=0, then |z2z3|2+|z3z1|2+|z1z2|2 equals

A
13|z1|2+2|z2|2+2|z3|2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
23(|z1|2+|z2|2+|z3|2)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
2(|z1|2+|z2|2+|z3|2)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
3(|z1|2+|z2|2+|z3|2)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D 3(|z1|2+|z2|2+|z3|2)
Given that, z1+z2+z3=0 ....(1)
Let a=|z2z3|2+|z3z1|2+|z1z2|2
a=(z2z3)(¯z2¯z3)+(z3z1)(¯z3¯z1)+(z1z2)(¯z1¯z2)
a=2(|z2|2+|z3|2+|z1|2)[¯z2(z1+z3)+¯z3(z1+z2)+¯z1(z3+z2)]
a=2(|z2|2+|z3|2+|z1|2)+(¯z2z2+¯z3z3+¯z1z1) ....[ Using (1)]

a=3(|z2|2+|z3|2+|z1|2)
Ans: D

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