Simplify i^5

Problem

i5

Solution

1. Identify the property of the imaginary unit i where i=√(,−1) and i2=−1

2. Rewrite the expression by breaking the exponent into a power of 2 to utilize the known value of i2

i5=i4⋅i1

3. Express i4 as a power of i2 to simplify the calculation.

i5=(i2)2⋅i

4. Substitute −1 for i2 into the expression.

i5=(−1)2⋅i

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

i5=1⋅i

i5=i

Final Answer

i5=i

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