Simplify i^5*9

Problem

i5⋅9

Solution

1. Identify the properties of the imaginary unit i where i2=−1

2. Simplify the power of i by using the cycle of powers: i1=i i2=−1 i3=−i and i4=1

3. Rewrite i5 as a product of i4 and i

i5=i4⋅i

4. Substitute the value i4=1 into the expression.

i5=1⋅i

i5=i

5. Multiply the simplified result by 9

i⋅9=9*i

Final Answer

i5⋅9=9*i

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