Show that the points `1, (-1)/2 + i (sqrt3)/2 ,and (-1)/2 - i (sqrt(3))/(2)` are the vertices of an equilateral triangle.

Prove that the points (0,0) (3, sqrt(3)) and (3, -sqrt(3)) are the vertices of an equilateral triangle.

Show that the complex numbers 3+3i , -3-3i(-3sqrt(3)+i3sqrt(3)) are the vertices of an equilateral triangle in the complex plane.

Prove that (sqrt(2),sqrt(2)) (-sqrt(2), -sqrt(2) ) and (-sqrt(6 ) , sqrt(6)) are ther vertices of an equilateral triangle.

Show that the point (3,-2),(3,2),(-1,2) and (-1,-2) taken in order are the vertices of a square.

Show that cot (7 (1)/(2)) = sqrt(2) + sqrt(3) + sqrt(4) + sqrt(6) .

Show that the points A (1,1,1), B (1,2,3) and C (2,-1,1) are vertices of an isosceles triangle.

Show that ( 2 + i sqrt(3))^(10) - (2 - i sqrt(3))^(10) is purely imaginary.

Show that ((sqrt(3))/(2) + (i)/(2))^(5) + ((sqrt(3))/(2) - (i)/(2))^(5) = -sqrt(3)

The value of ((1+sqrt(3)i)/(1 - sqrt(3)i))^(10) is