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  4. If |z1|=|z2|=|z3|=1 and z1, z2, z3 are represented by the vertices of an equilateral triangle then

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Q. If $\left|z_1\right|=\left|z_2\right|=\left|z_3\right|=1$ and $z_1, z_2, z_3$ are represented by the vertices of an equilateral triangle then

Complex Numbers and Quadratic Equations

Solution:

All the three vertices lies on circle $|z|=1$
so there centroid at $O$ i.e.
$\frac{z_1+z_2+z_3}{3}=0$