A value of n such that `((sqrt(3))/(2)+(i)/(2))^(n)=1` is
(A) 12 (B) 3 (C) 2 (D) 1

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

Let (:a_(n):) be a sequence given by a_(n+1)=3a_(n)-2*a_(n-1) and a_(0)=2,a_(1)=3 then the value of sum_(n=1)^(oo)(1)/(a_(n)-1) equals (A) 1 (B) (1)/(2) (C) 2 D) 4

Let n be a positive integer such that sin (pi/(2n))+cos (pi/(2n))= sqrt(n)/2 then (A) n=6 (B) n=1,2,3,….8 (C) n=5 (D) none of these

The least positive value of n forwhich [(i(i+sqrt(3)))/(1-i^(2))]^(n) is a positive integer is

Integer just greater tehn (sqrt(3)+1)^(2n) is necessarily divisible by (A) n+2 (B) 2^(n+3) (C) 2^n (D) 2^(n+1)

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

sum_(n=1)^oo sin^-1( (sqrt(n)-(sqrt(n-1)))/(sqrt((n)(n+1)) )= (A) pi/4 (B) pi/2 (C) - pi/3 (D) pi/3