# How do you simplify  i^-6 ?

Feb 8, 2016

$- 1$

#### Explanation:

First, recognize the powers of $i$:

$\left\{\begin{matrix}i = \sqrt{- 1} \\ {i}^{2} = {\left(\sqrt{- 1}\right)}^{2} = - 1 \\ {i}^{4} = {\left({i}^{2}\right)}^{2} = {\left(- 1\right)}^{2} = 1\end{matrix}\right.$

Note that ${i}^{-} 6 = \frac{1}{i} ^ 6$.

${i}^{-} 6 = \frac{1}{i} ^ 6 = \frac{1}{{i}^{4} \left({i}^{2}\right)} = \frac{1}{1 \left(- 1\right)} = - 1$