# If the complex numbers z1 ,z2 ,z3 represent the vertices of an equilateral triangle and |z1|=|z2|=|z3| , then z1+z2+z3=?

Solution:   Given ,     $\left | z_{1} \right |=\left | z_{2} \right |=\left | z_{3} \right |$

$\Rightarrow$     origin is equidistant from $z_{1},z_{2},z_{3}$

$\Rightarrow$         Origin is the circumcentre of equilateral triangle with vertices $z_{1},z_{2},z_{3}$

$\Rightarrow$        $\frac{z_{1}+z_{2}+z_{3}}{3}=0\Rightarrow z_{1}+z_{2}+z_{3}=0$

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