Passage: If z_1 , z_2 and z_3 are three complex numbers representing the points A, B and C, respectively, in the Argands plane and ∠BAC=α, then ((z_3 −z_1 )/(z_2 −z_1 ))=(((AC)/(AB)))(cosα+isinα) (i) If the roots of the equation z^3 +3a_1 z^2 +3a_2 z+a_3 =0 represent the vertices of an equilateral triangle, then (A) a_1 ^2 =a_3 (B) a_1 ^2 =a_2 (C) a_1 ^2 =a_2 a_3 (D) a_1 ^3 =a_2 a


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Question Number 140260 by EnterUsername last updated on 05/May/21

$Passage : If z_{1}, z_{2} and z_{3} are three complex numbers$ $representing the points A, B and C, respectively, in the$ $Argands plane and ∠ B A C = α, then$ $\frac{z_{3} - z_{1}}{z_{2} - z_{1}} = (\frac{A C}{A B}) (\cos α + i \sin α)$ $(i) If the roots of the equation$ $z^{3} + 3 a_{1} z^{2} + 3 a_{2} z + a_{3} = 0$ $represent the vertices of an equilateral triangle, then$ $(A) a_{1}^{2} = a_{3} (B) a_{1}^{2} = a_{2}$ $(C) a_{1}^{2} = a_{2} a_{3} (D) a_{1}^{3} = a_{2} a_{3}$
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