Simplify i^5*1

Problem

i^5⋅1

Solution

1. Identify the identity property of multiplication, which states that any value multiplied by 1 remains unchanged.

i^5⋅1=i^5

2. Recall the definition of the imaginary unit i where i^2=−1

i^2=−1

3. Rewrite the expression i^5 using the properties of exponents to isolate powers of i^2 or i^4

i^5=i^4⋅i

4. Evaluate i^4 by squaring i^2

i^4=(i^2)^2=(−1)^2=1

5. Substitute the value of i^4 back into the expression to find the final simplified form.

1⋅i=i

Final Answer

i^5⋅1=i

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