Simplify i^28

Problem

i28

Solution

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

i1=i

i2=−1

i3=−i

i4=1

2. Determine the remainder when the exponent is divided by 4 because the powers of i repeat every 4 terms.

28÷4=7

28=4×7+0

3. Apply the property of exponents to rewrite the expression using the power of i4

i28=(i4)7

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

i28=(1)7

5. Simplify the result.

1=1

Final Answer

i28=1

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