The expression `(1+i)^(n_1)+(1+i^(3))^(n_(2))` is real iff

For positive integers n_(1), 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)) , where i= sqrt-1 is a real number if and only if

The expression ((1+i)^(n))/((1-i)^(n-2)) equals

The expression ((1+i)^(n))/((1-i)^(n-2)) equals

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

The expression frac{(1+i)^n}{(1-i)^(n-2)} equals

For positive integers n_1,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) , where i= sqrt(-1) is a real number 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 :