Simplify i^32

Problem

i32

Solution

1. Identify the pattern 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 four terms.

32÷4=8

32=4×8+0

3. Apply the property of exponents to rewrite the expression using the power of 4

i32=(i4)8

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

i32=(1)8

5. Simplify the result.

1=1

Final Answer

i32=1

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