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.

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 is equal to -1 when n is any other positive integer.

Prove that ((-1 + isqrt3)/(2))^(n) + ((-1-isqrt3)/(2))^(n) is equal to 2 if n be a multiple of 3 and is equal to -1 if n be any other integer

If (sqrt(3)-i)^(n)=2^(n) , n in Z, then n is a multiple of

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

Prove that ((-1+sqrt(-3))/(2))^(n)+((-1-sqrt(-3))/(2))^(n) =2, when n is positive integer multipel of 3, =-1 when n is positive integer but not a multiple of 3.

If ((1+i sqrt(3))/(1-i sqrt(3)))^(n) is an integer, then n=

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

((1+i sqrt(3))/(1-i sqrt(3)))^(n) is an integer,then n is

If (sqrt(3)-i)^(n)=2^(n),n in I, the set of integers, then n is a multiple of