Answer
$-i$
Work Step by Step
We know that $i^{2}=-1$. Therefore, $i^{4}=i^{2}\times i^{2}=-1\times-1=1$.
We can use the fact that $i^{4}=1$ in order to evaluate higher powers of $i$.
$i^{-13}=i^{-13}\times (i^{4})^{4}=i^{-13}\times i^{16}=i^{3}=i^{2}\times i=-1\times i=-i$