Simplify i^35

Problem

i35

Solution

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

2. Recall that i1=i i2=−1 i3=−i and i4=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.

i35=i(4×8+3)

i35=(i4)8×i3

5. Substitute the known values i4=1 and i3=−i into the expression.

i35=(1)8×(−i)

6. Simplify the final result.

i35=1×−i

i35=−i

Final Answer

i35=−i

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