Simplify i^5*5

Problem

i^5⋅5

Solution

1. Identify the properties of the imaginary unit i where i^2=−1

2. Determine the value of i^5 by using the cyclic nature of powers of i which repeat every four powers: i^1=i i^2=−1 i^3=−i and i^4=1

3. Rewrite the power as i^5=i^4⋅i

4. Substitute the known value i^4=1 into the expression.

i^5=1⋅i

i^5=i

5. Multiply the result by the constant 5.

i⋅5=5*i

Final Answer

i^5⋅5=5*i

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