How do you simplify i^7?

Feb 7, 2016

${i}^{7} = - i$

Explanation:

${i}^{7} = {\left({i}^{2}\right)}^{3} \times i$

$\textcolor{w h i t e}{\text{XXX}} = {\left(- 1\right)}^{3} \times i$

$\textcolor{w h i t e}{\text{XXX}} = {\left(- 1\right)}^{2} \times \left(- 1\right) \times i$

$\textcolor{w h i t e}{\text{XXX}} = 1 \times \left(- 1\right) \times i$

$\textcolor{w h i t e}{\text{XXX}} = - i$