If two vertices of an equilateral triangle are `z_1,z_2` then find the complex number `z_3` represented by the third vertex where `z_1`, `z_2,z_3` are anticlockwise.

z_1,z_2 are represented by two consecutive vertices of a rhombus, the angle at z_1 being pi/4 . Find the complex numbers z_3,z_4 represented by the other vertices, the vertices z_1,z_2,z_3,z_4 being in the anticlockwise sense and origin being the center.

If z_(1),z_(2),z_(3) be vertices of an equilateral triangle occurig in the anticlockwise sense, then

Let z_1,z_2,z_3 be three distinct non zero complex numbers which form an equilateral triangle in the Argand pland. Then the complex number associated with the circumcentre of the tirangle is (A) (z_1 z_2)/z_3 (B) (z_1z_3)/z_2 (C) (z_1+z_2)/z_3 (D) (z_1+z_2+z_3)/3

Complex number z_1, z_2 and z_3 in AP

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