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 is a positive integer, then (1+i)^n+(1-i)^n=

If n is a positive integer, then (1+i)^(n)+(1-i)^(n)=

(1+i)^(n_1)+(1+i^3)^(n_1)+(1+i^5)^(n_2)+(1+i^7)^(n_2) is a real number if

If n is a positive integer,then (1+i)^(n)+(1-1)^(n) is equal to

If n is a positive integer, show that (1 + i)^(n) + (1 - i)^(n) = 2 ^((n+2)/2) cos ((npi)/4) .

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

For positive integer n_1,n_2 the value of the expression (1+i)^(n1) +(1+i^3)^(n1) (1+i^5)^(n2) (1+i^7)^(n_20), where i=sqrt-1, is a real number if and only if (a) n_1=n_2+1 (b) n_1=n_2-1 (c) n_1=n_2 (d) n_1 > 0, n_2 > 0

For positive integer n_1,n_2 the value of the expression (1+i)^(n1) +(1+i^3)^(n1) (1+i^5)^(n2) (1+i^7)^(n_20), where i=sqrt-1, is a real number if and only if (a) n_1=n_2+1 (b) n_1=n_2-1 (c) n_1=n_2 (d) n_1 > 0, n_2 > 0

For positive integers n_(1) and n_(2) the value of the expression (1+i)^(n_(1))+(1+i^(3))^(n_(1))+(1+i^(5))^(n_(2))+(1+i^(7))^(n_(2)) is a real number if and only if