Answer:
-1
Step-by-step explanation:
Note that [tex]i+i^2+i^3+i^4 = i-1-i+1 = 0[/tex], and this means that every 4 terms, the terms cancel to 0. Therefore, by taking modulo 4, we only need to find [tex]i^{257}+i^{258}+i^{259} = i-1-i = -1[/tex] since $i$ has a cycle of 4.
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Answer:
-1
Step-by-step explanation:
Alternate terms have a sum of zero:
i^n +i^(n+2) = (i^n)(1 +i^2) = (i^n)(1 -1) = 0
So, the sum to i^256 is zero, and i^257 +i^259 = 0. The value of the sum is then i^258 = i^(258 mod 4) = i^2 = -1
The given expression evaluates to -1.
