[" If "n_(1),n_(2)" are positive integers,then "(1+i)^(n_(1))+(1+i^(3))''],[+(1+i^(5))^(n_(2))+(1+i^(7))^(n_(2))" is 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 :

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

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

(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-i)^n=

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