Find z so that z+1,z+2,z+3 are consecutive terms of a geometric progression.

Find y so that y,y+2,y+3 are consecutive terms of a geometric progression.

If z_1,z_2,z_3 are the vertices of a triangle then its centroid is

Assertion (A) : The origin and the roots of the equation x^(2) + ax + b = 0 form an equilateral triangle if a^(2) = 3b Reason (R) : If z_(1) , z_(2) , z_(3) are vertices of an equilateral triangle then z_(1)^(2) + z_(2)^(2) + z_(3)^(2) = z_(1) z_(2) + z_(2) z_(3) + z_(3) z_(1)

If the complex numbers z_(1) , z_(2) , z_(3) represents the vertices of an equilateral triangle such that |z_1| = |z_2| = |z_3| then

A : If 2z_1-3z_2+z_3=0 then z_1,z_2,z_3 are collinear points R : If a , b, c inR such that a + b+ c = 0 and az_1+bz_2+cz_3=0 then z_1,z_2,z_3 are collinear

Let the complex number z_1,z_2,z_3 be the vertices of an equilateral triangle . Let z_0 be the circumcentre of the triangle . Then z_1^2+z_2^2+z_3^2=

If x,y,z are the three geometric means between 6,54, then z =

If z_(1) , z_(2) , z_(3) are the vertices of an equilateral triangle with centroid at z_0 show that z_(1)^(2) + z_(2)^(2) + z_(3)^(2) = 3 z_(0)^(2)

Let the complex number z_(1) , z_(2) , z_(3) be the vertices of an equilateral triangle . Let z_(theta) be the circumcentre of the triangle . Then z_(1)^(2) + z_(2)^(2) + z_(3)^(2) =

The condition for the points z_1,z_2,z_3,z_4 taken in order in the Argand plane to be the vertices of a parallelogram is