`i^(n+100)+i^(n+50)+i^(n+48)+i^(n+46)`

For an positive integer n, prove that : i^(n) + i^(n+1) + i^(n+2) + i^(n+3) + i^(n+4) + i^(n + 5) + i^(n+6) + i^(n+7) = 0 .

If i= sqrt-1 and n is a positive integer , then i^(n) + i^(n + 1) + i^(n + 2) + i^(n + 3) is equal to

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

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

For any positive integer n, find the value of i^(n)+i^(n+1)+i^(n+2)+i^(n+3)+i^(n+4)+i^(n+5)+i^(n+6)+i^(n+7) .

For any positive integer n, prove that: i^(n)+i^(n+1)+i^(n+2)+i^(n+3)+i^(n+4)+i^(n+5)+i^(n+6)+i^(n+7)=0 .