`i^(n) + i^(n+1) + i^(n + 2) + i^(n + 3)`

1 + i^(2n) + i^(4n) + i^(6n)

The value of 1/(i^n) + 1/(i^(n + 3)) + 1/(i^(n + 2)) + 1/(i^(n + 1)) is :

Matrix A such that A^(2) = 2A - I , where I is the identity matrix, then for n ge 2, A^(n) is equal to a) 2^(n - 1) A - (n - 1) I b) 2^(n - 1)A - I c) n A - (n - 1) I d) nA - I

Find the value of ( i^2 + n ) ( i^2 + n - 1 ) ( i^2 + n - 2 ) .......( i^2 + 1 )

The value of i^(2n)+i^(2n+1)+i^(2n+2)+i^(2n+3), where i=sqrt(-1), is

If n_1, n_2 are positive integers, then (1 + i)^(n_1) + ( 1 + i^3)^(n_1) + (1 + i^5)^(n_2) + (1 + i^7)^(n_2) is real if and only if :

If n_1, n_2 are positive integers, then (1 + i)^(n_1) + ( 1 + i^3)^(n_1) + (1 + i_5)^(n_2) + (1 + i^7)^(n_2) is real if and only if :

If n_1, n_2 are positive integers, then (1 + i)^(n_1) + ( 1 + i^3)^(n_1) + (1 + i_5)^(n_2) + (1 + i^7)^(n_2) is real if and only if :

Statement - I : If n = 4m + 3 , is integer then i^(n) is equal to -i Statement- II : If n in N then (1 + i)^(2n) + (1- i)^(2n) is purely real number