Let the complex numbers \[{{z}_{1}},{{z}_{2}}\] and \[{{z}_{3}}\] be the vertices of an equilateral triangle. Let \[{{z}_{0}}\]be the circumcentre of the triangle, then \[z_{1}^{2}+z_{2}^{2}+z_{3}^{2}=\] [IIT 1981]

Let the complex numbers \[{{z}_{1}},{{z}_{2}}\] and \[{{z}_{3}}\] be t

1.	Let the complex numbers \[{{z}_{1}},{{z}_{2}}\] and \[{{z}_{3}}\] be the vertices of an equilateral triangle. Let \[{{z}_{0}}\]be the circumcentre of the triangle, then \[z_{1}^{2}+z_{2}^{2}+z_{3}^{2}=\] [IIT 1981]
A.	\[z_{0}^{2}\]
B.	\[-z_{0}^{2}\]
C.	\[3z_{0}^{2}\]
D.	\[-3z_{0}^{2}\]
Answer» D. \[-3z_{0}^{2}\]