# How do you simplify i^-11?

Simplify the expression by using the fact that ${i}^{4} = 1$ to find
${i}^{- 11} = i$
Using that ${i}^{2} = - 1$ and thus ${i}^{4} = {\left({i}^{2}\right)}^{2} = 1$ we have
${i}^{-} 11 = \frac{1}{i} ^ 11 = \frac{i}{i \cdot {i}^{11}} = \frac{i}{i} ^ 12 = \frac{i}{{i}^{4}} ^ 3 = \frac{i}{1} ^ 3 = \frac{i}{1} = i$