# How do you simplify i^266?

Jan 20, 2016

$- 1$

#### Explanation:

The powers of $i$ go as follow:

• $i = \sqrt{- 1}$
• ${i}^{2} = - 1$
• ${i}^{4} = {\left({i}^{2}\right)}^{2} = 1$

Thus, we can rewrite ${i}^{266}$ in terms of these:

${i}^{266} = {\left({i}^{4}\right)}^{66} \left({i}^{2}\right) = {\left(1\right)}^{66} \left(- 1\right) = - 1$