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

If |z1|=|z2|=|z3| and z1,z2,z3 are vertices of an equilateral triangle, then what is the value of z1+z2+z3

A
0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
3
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 C 0
If A=z1, B=z2 and C=z3 are vertices of the triangle, then its centroid G will be (z1+z2+z3)3

Now,|z1|=|z2|=|z3|=> the points A,B,C lie on a circle with centre as the origin O.
Therefore, O is the circumcentre of the triangle.

But for an equilateral triangle, the circumcentre coincides with the centroid.
Therefore, the centroid of the triangle is O
or
(z1+z2+z3)3=0
or
(z1+z2+z3)=0

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Geometric Representation and Trigonometric Form
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon