. Example . Suppose z , and are the vertices of an equilateral triangle inscribed in the circle z = . If z , then find z z = represents the circle with centre ( , ) and radius .
Let A, B, and C be the vertices of the given triangle. Since the vertices z , and form an equilateral triangle inscribed in the circle z = , the sides of this triangle AB, BC, and CA subtend p radians ( degree) at the origin (circumcenter of the triangle). (The complex number z e i θ is a rotation of z by θ radians in the counter clockwise direction about the origin.) Therefore, we can obtain z by the rotation of z by p and p respectively. Given that OA = z ; OB = z e e = = ; Re Im O = + z = − B C Fig.
. - - OC = z e z e e Therefore, z = , and z