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If z(1),z(2),z(3) are the vertices of a...

If `z_(1),z_(2),z_(3)` are the vertices of an equilational triangle ABC such that `|z_(1)-i|=|z_(2)- i| = |z_(3)-i|,` then `|z_(1)+z_(2)+z_(3)|` equals to

A

`3sqrt(3)`

B

`sqrt(3)`

C

3

D

`(1)/(3sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
`|z_(1)-i| = |z_(2) - p| = |z_(3) -i|`
Hence, `z_(1),z_(2),z_(3)` lie on the circle whose centre is I . Also given that the triangle is equilarteral. Hence, centroid and circumcentre conicides.
`therefore (z_(1) + z_(2) + z_(3))/(3) = i`
` rArr |z_(1) + z_(2) + z_(3)|=3`
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