1
Question
If z1, z2, z3 are vertices of an equilateral triangle ABC such that |z1−i|=|z2−i|=|z3−i|, then |z1+z2+z3| equals to
If z1, z2, z3 are vertices of an equilateral triangle ABC such that |z1−i|=|z2−i|=|z3−i|, then |z1+z2+z3| equals to
Open in App
Solution
The correct option is C 3
Given that,
|z1−i|=|z2−i|=|z3−i|
Hence, z1, z2, z3 lie on a circle whose centre is i.
Also, given that the triangle is equilateral. Hence, centroid and circumcenter coincides.
∴z1+z2+z33=i
⇒|z1+z2+z3|=3
Given that,
|z1−i|=|z2−i|=|z3−i|
Hence, z1, z2, z3 lie on a circle whose centre is i.
Also, given that the triangle is equilateral. Hence, centroid and circumcenter coincides.
∴z1+z2+z33=i
⇒|z1+z2+z3|=3
Suggest Corrections
1
Similar questions
View More
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
