Simplify i^2+i^8

Problem

i^2+i^8

Solution

1. Identify the powers of the imaginary unit i where i=√(,−1)

2. Evaluate the first term using the definition i^2=−1

3. Simplify the second term by using the property that powers of i repeat every four cycles, specifically i^4=1

4. Apply the exponent rule to rewrite i^8 as (i^4)^2

i^8=(1)^2

i^8=1

5. Substitute the simplified values back into the original expression.

−1+1

6. Combine the terms to find the final sum.

−1+1=0

Final Answer

i^2+i^8=0

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