If n is a positive integer , then `(sqrt(3)+1)^(2n)-(sqrt(3)-1)^(2n)` is -

If n is a positive interger,them (sqrt(5)+1)^(2n+1)-(sqrt(5)-1)^(2n-1) is

If n is a positive integer,then (sqrt(3)+i)^(n)+(sqrt(3)-i)^(n) is

If n is a possible integer, then (sqrt3+1)^(2n)-(sqrt3-1)^(2n) is

The least positive integer n for which (sqrt(3)+i)^(n)=(sqrt(3)-i)^(n) is

Prove that (a)(1+i)^(n)+(1-i)^(n)=2^((n+2)/(2))*cos((n pi)/(4)) where n is a positive integer. (b) (1+i sqrt(3))^(n)+(1-i sqrt(3)^(n)=2^(n+1)cos((n pi)/(3)), where n is a positive integer

If n is a positive integer and U_(n) = (3 + sqrt5)^(n) + (3 - sqrt5)^(n) , then prove that U_(n + 1) = 6U_(n) - 4U_(n -1), n ge 2

The least positive integer n for which ((1+sqrt(3)i)/(1-sqrt(3)i))^(n) = 1 , is