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

If (sqrt3-i)^n=2^n,b epsilon 1 ,the set of integers,then n is a multiple of

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

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

If (sqrt(3)+i)^(n)=x_(n)+iy_(n) and n is a positive integer then the value of x_(n-1)y_(n)-x_(n)y_(n-1)=

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

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.

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.

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.

Select and write the correct answer from the given alternatives in each of the following: If i = sqrt(-1) and n is a positive integer, then i^n + i^(n+1) + i^(n+2) + i^(n+3) =