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

If z1,z2 and z3 are complex numbers such that

|z1|=|z2|=|z3|=1z1+1z2+1z3=1,

then |z1+z2+z3|


A

Equal to 1

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

Less than 1

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

Greater than 3

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

Equal to 3

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

The correct option is A

Equal to 1


1=1z1+1z2+1z3=z1¯z1z1+z2¯z2z2+z3¯z3z3

(hence, |z1|2=1=z1¯¯¯¯¯z1, etc)

|z1+z2+z3|=|¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯z1+z2+z3|= |z1+z2+z3|

(hence,|¯¯¯¯¯z1|=|z1|)


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