Simplify i^35

Problem

i^35

Solution

1. Identify the cycle of the powers of the imaginary unit i

2. Recall that i^1=i i^2=−1 i^3=−i and i^4=1

3. Divide the exponent by 4 to find the remainder, since the powers of i repeat every 4 terms.

35=4×8+3

4. Apply the property of exponents to rewrite the expression using the remainder.

i^35=i^(4×8+3)

i^35=(i^4)^8×i^3

5. Substitute the known values i^4=1 and i^3=−i into the expression.

i^35=(1)^8×(−i)

6. Simplify the final result.

i^35=1×−i

i^35=−i

Final Answer

i^35=−i

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