Find the value of `i^n+i^(n+1)+i^(n+2)+i^(n+3)`

For a positive integer n , find the value of (1-i)^(n) (1 - 1/i)^(n)

Find the value of 1+i^(2)+i^(4)+i^(6)+...+i^(2n), where i=sqrt(-1) and n in N.

Find the value of 1+i^2+i^4+i^6++i^(2n)

If Sigma_( i = 1)^( 2n) sin^(-1) x_(i) = n pi , then find the value of Sigma_( i = 1)^( 2n) x_(i) .

Find the value of n if: (i) (n+2)! = 12n! (ii) (n+2)! = 60(n-1)! (iii) (n+3)! = 2550 (n+1)! (iv) (n-2)! = 132. (n-4)! .

If m,n,p,q are consecutive integers then the value of i^(m)+i^(n)+i^(p)+i^(q) is

If Sigma_(i=1)^(2n) cos^(-1) x_(i) = 0 ,then find the value of Sigma_(i=1)^(2n) x_(i)

For a positive integer n , find the value of ( 1-i)^n(1-1/i)^ndot

If x_(1), x_(2), ………,x_(n) are n values of a variable x such that sum(x_(i)-3) = 170 and sum(x_(i)-6) = 50. Find the value of n and the mean of n values.

If n is any positive integer, write the value of (i^(4n+1)-i^(4n-1))/2 .