Simplify i^11

Problem

i11

Solution

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

i1=i

i2=−1

i3=−i

i4=1

2. Divide the exponent by 4 to find the remainder, since the powers of i repeat every 4 terms.

11=4×2+3

3. Rewrite the expression using the properties of exponents.

i11=i(4×2+3)

i11=(i4)2×i3

4. Substitute the known values for i4 and i3

i11=(1)2×(−i)

5. Simplify the final result.

i11=1×−i

i11=−i

Final Answer

i11=−i

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