question_answer

Let the complex numbers \[{{z}_{1}},\] \[{{z}_{2}}\] and \[{{z}_{3}}\] be the vertices of an equilateral triangle. Let \[{{z}_{0}}\] be the circumventer of the triangle, then \[{{z}_{1}}^{2}+{{z}_{2}}^{2}+{{z}_{3}}^{2}=\]

A)  \[3\,{{z}_{0}}^{2}\]

B)  \[-\,3\,{{z}_{0}}^{2}\]

C)  \[{{z}_{0}}^{2}\]                              

D)  \[-\,{{z}_{0}}^{2}\]

E)  None of these