If \( z_{1}, z_{2}, z_{3} \) are the vertices of an equilateral triangle in the argand plane, th....

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If \( z_{1}, z_{2}, z_{3} \) are the vertices of an equilateral triangle
\( \mathrm{P} \)
in the argand plane, then
W
\( \left(z_{1}^{2}+z_{2}^{2}+z_{3}^{2}\right)=k\left(z_{1} z_{2}+z_{2} z_{3}+z_{3} z_{1}\right) \) is true for
(1) \( k=1 \)
(2) \( k=2 \)
(3) \( k=3 \)
(4) \( k=4 \)


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