If the complex numbers z_1, z_2, z_3 represen | vedclass

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(A) Let the complex numbers $z_1, z_2, z_3$ denote the vertices $A, B, C$ of an equilateral triangle $ABC$.Since $|z_1| = |z_2| = |z_3|$,the origin $O

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(A) Let the complex numbers $z_1, z_2, z_3$ denote the vertices $A, B, C$ of an equilateral triangle $ABC$.Since $|z_1| = |z_2| = |z_3|$,the origin $O$ is equidistant from all vertices $A, B, C$.This implies that the origin $O$ is the circumcenter of the equilateral triangle $ABC$.For an equilateral triangle,the circumcenter,centroid,and orthocenter coincide.If $G$ is the centroid,then $G = \frac{z_1 + z_2 + z_3}{3}$.Since the centroid $G$ coincides with the circumcenter $O$ (which is the origin $0$),we have $\frac{z_1 + z_2 + z_3}{3} = 0$.Therefore,$z_1 + z_2 + z_3 = 0$.

If the complex numbers $z_1, z_2, z_3$ represent the vertices of an equilateral triangle such that $|z_1| = |z_2| = |z_3|$,then $z_1 + z_2 + z_3 = $

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