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 $i$.
$\frac{1}{i^{-11}}=i^{11}=i^{8}\times i^{2}\times i=(i^{4})^{2}\times-1\times i=(1)^{2}\times-1\times i=1\times-1\times i=-i$