((-1+i sqrt(3))/(2))^(3n)+((-1-i sqrt(3))/(2))^(3n)=

((-1+i sqrt(3))/(2))^(3 n)+((-1-i sqrt(3))/(2))^(3 n)=

the value of ((-1+sqrt(3)i)/(2))^(3n)+((-1-sqrt(3)i)/(2))^(3n)=

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

Show that ((-1+sqrt(3)i)/(2))^(n)+((-1-sqrt(3i))/(2))^(n) is equal to 2 when n is a multiple of 3 and 3 is equal to -1 when n is any other positive integer.

What is the value of ((1=-+isqrt3)/(2))^(3n)+((-1+isqrt3)/(2))^(3n) where i=sqrt(-1) ?

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)