Simplify i^25

Problem

i25

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.

25÷4=6* remainder *1

3. Rewrite the expression using the property of exponents in=i(4*k+r)=(i4)k⋅ir

i25=i(4*(6)+1)

4. Substitute i4=1 into the expression.

i25=(i4)6⋅i1

i25=(1)6⋅i

5. Simplify the final result.

i25=1⋅i

i25=i

Final Answer

i25=i

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