Im confused i tried the power thing but how do you compute at the end

Because \((i, i^2, i^3, i^4) = (i, -1, -i, 1)\), we have  \(i + i^2 + i^3 \cdots + i^{258} + i^{259} = 64(i - 1 - i + 1) + i^{257} + i^{258} + i^{259}\). So, the desired sum is \(i^{257} + i^{258} + i^{259} = i - 1 - i = \boxed{-1}\).