A) \[{{z}_{1}}+{{z}_{2}}+{{z}_{3}}\le 0\]
B) \[{{z}_{1}}+{{z}_{2}}+{{z}_{3}}\ge 0\]
C) \[{{z}_{1}}+{{z}_{2}}+{{z}_{3}}=0\]
D) None of these
Correct Answer: C
Solution :
Given, \[|{{z}_{1}}|=|{{z}_{2}}|=|{{z}_{3}}|\] Three points lies on the circle, whose centre is origin. Since, these points are vertices of an equilateral triangle so orthocentre and circumcentre will be same. Hence, \[\frac{{{z}_{1}}+{{z}_{2}}+{{z}_{3}}}{3}=0\] \[\Rightarrow \] \[{{z}_{1}}+{{z}_{2}}+{{z}_{3}}=0\]
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