Simplify i^8

Problem

i8

Solution

1. Identify the properties of the imaginary unit i where i2=−1

2. Determine the cycle of powers for i which repeats every four terms: i1=i i2=−1 i3=−i and i4=1

3. Rewrite the expression using the power of a power rule to utilize the fact that i4=1

i8=(i4)2

4. Substitute the value of i4 into the expression.

(1)2

5. Simplify the resulting numerical value.

1

Final Answer

i8=1

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