## Intermediate Algebra (6th Edition)

Here, we are using the pattern of squaring i. For example, $i^{1}=i$, $i^{2}=-1$, $i^{3}=-1\times i=-i$, $i^{4}=-i\times i=-i^{2}=-1\times-1=1$, and so on. Therefore, we can use the fact that $i^{4}=1$ and then rewrite the expression in terms of $i^{4}$ in order to simplify. $i^{10}=i^{8}\times i^{2}=(i^{4})^{2}\times i^{2}=(1)^{2}\times-1=1\times-1=-1$