If z1,z2,z3 are the vertices of an equilateral triangle ABC such that |z1−i|=|z2−i|=|z3−i|, then |z1+z2+z3| equals to
A
3√3
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B
√3
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C
3
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D
1√3
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Solution
The correct option is D3 Therefore, z1,z2,z3 are point equidistant from i. Hence they lie on a circle centered at i. Also z1,z2,z3 are vertices of an equilateral triangle. Hence centroid and the circumcentre coincides. z1+z2+z33=i |z1+z2+z3|=3|i| =3