Let `z_1` and `z_2` be the nth roots of unity which subtend a right angle at the origin then n must be the form

The locus of the midpoints of chords of the circle x^(2) + y^(2) = 1 which subtends a right angle at the origin is

Let the complex numbers z_1,z_2 and z_3 be the vertices of an equilateral triangle let z_0 be the circumcentre of the triangle then prove that z_1^2+z_2^2+z_3^2=3z_0^2

If z_(1) , z_(2) and z_(3) are the vertices of DeltaABC , which is not right angled triangle taken in anti-clock wise direction and z_(0) is the circumcentre, then ((z_(0)-z_(1))/(z_(0)-z_(2)))(sin2A)/(sin2B)+((z_(0)-z_(3))/(z_(0)-z_(2)))(sin2C)/(sin2B) is equal to

z_(1) and z_(2) are two non-zero complex numbers, they form an equilateral triangle with the origin in the complex plane. Prove that z_(1)^(2)-z_(1)z_(2)+z_(2)^(2)=0

If alpha is the nth root of unity then 1+2alpha+3alpha^2+…. to n terms equal to

Let z_(1) and z_(2) be the roots of z ^(2)+az+b=0 . If the origin, z_(1) and z_(2) form an equilateral triangle. Then-

let z_1 and z_2 be roots of the equation z^2+pz+q=0 where the coefficients p and q may be complex numbers let A and B represnts z_1 and z_2 in the complex plane if angleAOB=alpha ne 0 and OA=OB where 0 is the origin prove that p^2=4qcos^2(alpha/2)

If z=omega,omega^2 where omega is a non-real complex cube root of unity, are two vertices of an equilateral triangle in the Argand plane, then the third vertex may be represented by a, z=1 b. z=0 c. z=-2 d. z=-1

z_1, z_2 and z_3 are the vertices of an isosceles triangle in anticlockwise direction with origin as in center , then prove that z_2, z_1 and kz_3 are in G.P. where k in R^+dot

Let z_1 be a fixed point on the circle of radius 1 centered at the origin in the Argand plane and z_1 ne+-1 consider an equilateral triangle inscribed in the circle with z_1,z_2,z_3 as the vertices taken in the counter clockwise directtion then z_1z_2z_3 is equal to