Simplify i^-17

Problem

i(−17)

Solution

1. Apply the negative exponent rule to rewrite the expression as a fraction.

i(−17)=1/(i17)

2. Identify the cycle of the powers of i which repeats every 4 terms: i1=i i2=−1 i3=−i and i4=1

in=i(n* mod *4)

3. Divide the exponent 17 by 4 to find the remainder.

17=4×4+1

4. Simplify the power of i in the denominator using the remainder.

i17=i1=i

5. Substitute the simplified power back into the fraction.

1/(i17)=1/i

6. Rationalize the denominator by multiplying the numerator and denominator by i

1/i×i/i=i/(i2)

7. Substitute i2=−1 and simplify the final result.

i/(−1)=−i

Final Answer

i(−17)=−i

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