" Show that "((sqrt(3)+i)/(2))^(6)+((i-sqrt(3))/(2))^(6)=-2

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

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

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

((1)/(2)+sqrt(3)/(2)i)^(6)

Show that (sqrt3/2 + i/2)^3 = i

(sqrt(3)+i)^(6)+(sqrt(3)-i)^(6)=

((-1+i sqrt(3))/(2))^(6)+((-1-i sqrt(3))/(2))^(6)+((-1+i sqrt(3))/(2))^(5)+((-1-i sqrt(3))/(2))^(6)

If i=sqrt(-)1, then 4+5(-(1)/(2)+(i sqrt(3))/(2))^(334)+3(-(1)/(2)+(i sqrt(3))/(2))^(365) is equal to (1)1-i sqrt(3)(2)-1+i sqrt(3)(3)i sqrt(3)(4)-i sqrt(3)

Show that ((i + sqrt(3))/(-i + sqrt(3)))^(2omega) + ((i - sqrt(3))/(i + sqrt(3)))^(2omega) = -1