If z_1 , z_2 , and z_3 are the vertices of an equilateral triangle described in counterclock sense and w≠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) (1/(z_1 −z_2 ))+(1/(z_2 −z_3 ))+(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


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

$If z_{1}, z_{2}, and z_{3} are the vertices of an equilateral triangle$ $described in counterclock sense and w \neq 1 is a cube root$ $of unity, then$ $(A) z_{1} - z_{3} = (z_{3} - z_{2}) w$ $(B) z_{1} + z_{2} w + z_{3} w^{2} = 0$ $(C) \frac{1}{z_{1} - z_{2}} + \frac{1}{z_{2} - z_{3}} + \frac{1}{z_{3} - z_{1}} = 0$ $(D) z_{1}^{2} + z_{2}^{2} + z_{3}^{2} = z_{1} z_{2} + z_{2} z_{3} + z_{3} z_{1}$
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