Simplify i^9

Problem

i9

Solution

1. Identify the cycle of the powers of the imaginary unit i

2. Recall that i1=i i2=−1 i3=−i and i4=1

3. Divide the exponent by 4 to find the remainder, since the powers of i repeat every 4 terms.

9=4×2+1

4. Rewrite the expression using the properties of exponents.

i9=i(4×2+1)

i9=(i4)2×i1

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

i9=(1)2×i

6. Simplify the resulting value.

i9=1×i

i9=i

Final Answer

i9=i

Want more problems? Check here!