Let \( z_{1}, z_{2}, z_{3} \) be three distinct complex numbers sat...

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Let \( z_{1}, z_{2}, z_{3} \) be three distinct complex numbers satisfying, \( \left|z_{1}-1\right|=\left|z_{2}-1\right|=\left|z_{3}-1\right|=1 \). Let A. B \& C be the points representing vertices of equilateral triangle in the Argand plane corresponding to \( z_{1}, z_{2} \)
\( \mathrm{P} \) and \( z_{3} \) respectively. Which of the following are true
(A) \( z_{1}+z_{2}+z_{3}=3 \)
(B) \( z_{1}^{2}+z_{2}^{2}+z_{3}^{2}=3 \)
W
(C) area of triangle \( A B C=\frac{3 \sqrt{3}}{1} \)
(D) \( z_{1} z_{2}+z_{2} z_{3}+z_{3} z_{1}=1 \)
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