Simplify i^10

Problem

i10

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.

10÷4=2* remainder *2

3. Rewrite the expression using the property of exponents in=ir where r is the remainder.

i10=i2

4. Substitute the known value for i2

i2=−1

Final Answer

i10=−1

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