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Question
If z1,z2,z3 are the vertices of an equilateral △ABC such that |z1−i|=|z2−i|=|z3−i|, then |z1+z2+z3|=
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Solution
Given that
|z1−i|=|z2−i|=|z3−i|
Let A(z1),B(z2),C(z3)
here z1,z2,z3 are equidistanced from point a=0+i
∴a will be centriod of △ABC
as △ABC is equilateral triangle
∴z1+z2+z33=i
⇒|z1+z2+z3|=3
|z1−i|=|z2−i|=|z3−i|
Let A(z1),B(z2),C(z3)
here z1,z2,z3 are equidistanced from point a=0+i
∴a will be centriod of △ABC
as △ABC is equilateral triangle
∴z1+z2+z33=i
⇒|z1+z2+z3|=3
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