Simplify i^23

Problem

i23

Solution

1. Identify the cycle of the imaginary unit i The powers of i repeat every four terms: i1=i i2=−1 i3=−i and i4=1

2. Divide the exponent by 4 to find the remainder.

23÷4=5* remainder *3

3. Rewrite the expression using the properties of exponents.

i23=i(4*(5)+3)

4. Apply the rule i(4*n+r)=ir

i23=(i4)5⋅i3

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

i23=(1)5⋅(−i)

6. Simplify the final result.

i23=−i

Final Answer

i23=−i

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