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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Solution

The correct option is A 0
Let the complex number $z_{1}, z_{2}, z_{3}$ denote the vertices A, B, C of an equilateral triangle ABC. Then, if O be the origin we have $O A = z_{1}, O B = z_{2}, O C = z_{3}$
Therefore, $| z_{1} | = | z_{2} | = | z_{3} | \Rightarrow O A = O B = O C$
i.e., O is then circumcentre of $Δ$ ABC
Hence, $z_{1} + z_{2} + z_{3} = 0$

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