## Intermediate Algebra (12th Edition)

In order to calculate the larger powers of $i$, we can first calculate the values of $i$, $i^{2}$, $i^{3}$, and $i^{4}$. $i^{1}=i$ $i^{2}=i\times i=-1$ $i^{3}=i\times i^{2}=i\times-1=-i$ $i^{4}=i^{2}\times i^{2}=-1\times-1=1$ We can use these values and the rules of exponents to derive larger powers of $i$. Therefore, $i^{102}=i^{100}\times i^{2}=(i^{4})^{25}\times i^{2}=1^{25}\times-1=1\times-1=-1$.