Simplify i^17

Problem

i^17

Solution

1. Identify the cycle of the imaginary unit i The powers of i repeat every four terms: i^1=i i^2=−1 i^3=−i and i^4=1

2. Divide the exponent by 4 to find the remainder.

17÷4=4* remainder *1

3. Rewrite the expression using the property of exponents a^(m⋅n+r)=(a^n)^m⋅a^r

i^17=i^(4⋅4+1)

i^17=(i^4)^4⋅i^1

4. Substitute the known value i^4=1 into the expression.

i^17=(1)^4⋅i

5. Simplify the final result.

i^17=1⋅i

i^17=i

Final Answer

i^17=i

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