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-then-z-3-z-1-z-2-z-1-AC-

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}