If z 1 , z 2 and z 3 represent the vertices of an equilateral triangle such that z 1 = z 2 = z 3 then

Step-by-step solution

Since, z 1 = z 2 = z 3 . ⇒ z 1 - 0 = z 2 - 0 = z 3 - 0 . Thus, the given points are equidistant from origin, and we know that the point which is equidistant from the vertices of a triangle is the circumcentre of the triangle. ∴   0 is the circumcentre of an equilateral ∆ A B C and we also know that for an equilateral triangle the centroid and circumcentre are same. ∴   x 1 + x 2 + x 3 3 = 0 = y 1 + y 2 + y 3 3 where, z 1 = x 1 + i y 1 . ⇒ x 1 + x 2 + x 3 3 + i y 1 + y 2 + y 3