Simplify i^5*4

Problem

i^5⋅4

Solution

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

2. Simplify the power of i by using the cyclic nature of its powers: i^1=i i^2=−1 i^3=−i and i^4=1

3. Rewrite the expression i^5 as a product of i^4 and i

i^5=i^4⋅i

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

i^5=1⋅i

i^5=i

5. Multiply the simplified result by the constant 4.

i⋅4=4*i

Final Answer

i^5⋅4=4*i

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