Simplify i^5

Problem

i^5

Solution

1. Identify the property of the imaginary unit i where i=√(,−1) and i^2=−1

2. Rewrite the expression by breaking the exponent into a power of 2 to utilize the known value of i^2

i^5=i^4⋅i^1

3. Express i^4 as a power of i^2 to simplify the calculation.

i^5=(i^2)^2⋅i

4. Substitute −1 for i^2 into the expression.

i^5=(−1)^2⋅i

5. Simplify the result by calculating the square of −1

i^5=1⋅i

i^5=i

Final Answer

i^5=i

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