Simplify i^5*2

Problem

i^5⋅2

Solution

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

2. Simplify the power of i by dividing the exponent by 4 and finding the remainder.

3. Apply the power rule i^5=i^4⋅i^1

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

i^5=1⋅i

i^5=i

5. Multiply the simplified imaginary part by the constant 2.

i⋅2=2*i

Final Answer

i^5⋅2=2*i

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