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 I , the set of integers, then n is a multiple of

If i=sqrt(-1) , then (i^(n)+i^(-n), n in Z) is equal to

If i=sqrt(-1) , then (i^(n)+i^(-n), n in Z) is equal to

If z=-2+2sqrt(3)i, then z^(2n)+2^(2n)*z^n+2^(4n) is equal to

lim_(ntooo) (n(2n+1)^(2))/((n+2)(n^(2)+3n-1))" is equal to "

If n is a positive integer, then (sqrt(3)+1)^(2n)-(sqrt(3)-1)^(2n) is (1) an irrational number (2) an odd positive integer (3) an even positive integer (4) a rational number other than positive integers

If (5 + 2 sqrt(6))^(n) = I + f , where I in N, n in N and 0 le f le 1, then I equals

If x_1=sqrt(3) and x_(n+1)=(x_n)/(1+sqrt(1+x_ n^2)),AA n in N then lim_(n->oo)2^n x_n is equal to

If A= [(3 , -4), (1 , -1) ] , then prove that A^n=[(1+2n , -4n), (n , 1-2n) ] , where n is any positive integer.