If`(1+i)^(2n)+(1-i)^(2n)=-2^(n+1)(where,i=sqrt(-1)` for all those n, which are

(1+i)^(2 n)+(1-i)^(2 n), n in z is

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

Value of i^n+i^(n+1)+i^(n+2)+i^(n+3) (where i=sqrt-1 )

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,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 :

Show that (1-i)^(n)(1-(1)/(i))^(n)=2^(n) for all n in N

The value of the sume sum_(n=1)^(13) ( i^(n) + i^(n+1)) , where i = sqrt( -1) , equals :