The area of the triangle whose vertices are i, and ^2 is (Where is a complex cube root of unity other than 1, i is an imaginary number) ______ sq.units

Step-by-step solution

The area of a triangle with vertices at complex numbers i , , and ^2 can be found using their coordinates in the complex plane. Representing = ( 2 3 ) + i ( 2 3 ) , the points are A(0,1) , B(- 1 2 , 3 2 ) , and C(- 1 2 , - 3 2 ) . Since B and C share the same x -coordinate, the base BC is vertical with length 3 . The height from A to the line x = - 1 2 is 1 2 . 1 2 3 1 2 = 3 4 The area is 3 4 square units.