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Question Number 140107 by EnterUsername last updated on 04/May/21

If z_{1}, z_{2}, and z_{3} are the vertices of an equilateral triangle

described in counterclock sense and w \neq 1 is a cube root

of unity, then

(A) z_{1} - z_{3} = (z_{3} - z_{2}) w

(B) z_{1} + z_{2} w + z_{3} w^{2} = 0

(C) \frac{1}{z_{1} - z_{2}} + \frac{1}{z_{2} - z_{3}} + \frac{1}{z_{3} - z_{1}} = 0

(D) z_{1}^{2} + z_{2}^{2} + z_{3}^{2} = z_{1} z_{2} + z_{2} z_{3} + z_{3} z_{1}