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Question

If z1,z2,z3 are the vertices of an equilateral ABC such that |z1i|=|z2i|=|z3i|, then |z1+z2+z3|=

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Solution

Given that
|z1i|=|z2i|=|z3i|
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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