Simplify i^6

Problem

i6

Solution

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

2. Rewrite the expression using the laws of exponents to express i6 in terms of i2

i6=(i2)3

3. Substitute the value −1 for i2 into the expression.

(−1)3

4. Evaluate the power by multiplying −1 by itself three times.

−1⋅−1⋅−1=−1

Final Answer

i6=−1

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