Simplify i^8

Problem

i^8

Solution

1. Identify the properties of the imaginary unit i where i^2=−1

2. Determine the cycle of powers for i which repeats every four terms: i^1=i i^2=−1 i^3=−i and i^4=1

3. Rewrite the expression using the power of a power rule to utilize the fact that i^4=1

i^8=(i^4)^2

4. Substitute the value of i^4 into the expression.

(1)^2

5. Simplify the resulting numerical value.

1

Final Answer

i^8=1

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