The three angular points of a triangle are given by `Z=alpha, Z=beta,Z=gamma,w h e r ealpha,beta,gamma` are complex numbers, then prove that the perpendicular from the angular point `Z=alpha` to the opposite side is given by the equation `R e((Z-alpha)/(beta-gamma))=0`

the points (alpha,beta) , (gamma , delta) ,(alpha , delta) , (gamma , beta) are different real numbers are:

Let z_1 and z_2 q, be two complex numbers with alpha and beta as their principal arguments such that alpha+beta then principal arg(z_1z_2) is given by:

alpha, beta, gamma are real number satisfying alpha+beta+gamma=pi . The minimum value of the given expression sin alpha+sin beta+sin gamma is

If alpha , beta , gamma are the roots of the equation x^3 +px^2 +qx +r=0 then sum alpha^2 ( beta + gamma)=

Find the the image of the point (alpha, beta, gamma) with respect to the plane 2x+y+z=6 .

If alpha,beta,gamma in R, alpha+beta+gamma=4 " and " alpha^(2)+beta^(2)+gamma^(2)=6 , the number of integers lie in the exhaustive range of alpha is ……… .

If alpha,beta,gamma,delta are four complex numbers such that gamma/delta is real and alpha delta - beta gamma !=0 then z = (alpha + beta t)/(gamma+ deltat) where t is a rational number, then it represents:

If alpha,beta,gamma are the cube roots of p, then for any x,y,z (x alpha + y beta + z gamma)/(x beta + y gamma + z alpha =

If the complex numbers z_1,z_2,z_3 represents the vertices of a triangle ABC, where z_1,z_2,z_3 are the roots of equation z^3+3alphaz^2+3alphaz^2+3betaz+gamma=0, alpha,beta,gamma beng complex numbers and alpha^2=beta then /_\ABC is (A) equilateral (B) right angled (C) isosceles but not equilateral (D) scalene

If alpha, beta, gamma be the eccentric angles of three points of an ellipse, the normals at which are concurrent, show that sin(alpha+beta) + sin (beta+gamma) + sin (gamma + alpha) = 0 .