Simplify i^17

Problem

i17

Solution

1. Identify the cycle of the imaginary unit i The powers of i repeat every four terms: i1=i i2=−1 i3=−i and i4=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)=(an)m⋅ar

i17=i(4⋅4+1)

i17=(i4)4⋅i1

4. Substitute the known value i4=1 into the expression.

i17=(1)4⋅i

5. Simplify the final result.

i17=1⋅i

i17=i

Final Answer

i17=i

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