Simplify i^5*9

Problem

i^5⋅9

Solution

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

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

3. Rewrite 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 9

i⋅9=9*i

Final Answer

i^5⋅9=9*i

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