\( A B C D \) is a square with vertices \( A, B, C, D \) in anticlockwise sense. If \( A, B \) a....

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\( A B C D \) is a square with vertices \( A, B, C, D \) in
\( \mathrm{P} \)
anticlockwise sense. If \( A, B \) are represented by the complex numbers \( z_{1}, z_{2} \) respectively and the centroid of triangle \( B C D \) is represented by \( \alpha z_{1}+\beta z_{2} \), then \( \alpha \) is
(1) \( \left(\frac{1+2 i}{3}\right) \)
(2) \( \left(\frac{1-2 i}{3}\right) \)
(3) \( \left(\frac{2+2 i}{3}\right) \)
(4) \( \left(\frac{2-2 i}{3}\right) \)


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