Simplify i^5*1

Problem

i5⋅1

Solution

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

i5⋅1=i5

2. Recall the definition of the imaginary unit i where i2=−1

i2=−1

3. Rewrite the expression i5 using the properties of exponents to isolate powers of i2 or i4

i5=i4⋅i

4. Evaluate i4 by squaring i2

i4=(i2)2=(−1)2=1

5. Substitute the value of i4 back into the expression to find the final simplified form.

1⋅i=i

Final Answer

i5⋅1=i

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