Answer
$-i$
Work Step by Step
Knowing that $i^{2}=-1$, we also know that $i^{4}=(i^{2})^{2}=(-1)^{2}=1$. We can use the fact that $i^{4}=1$ to evaluate higher powers of $i$.
$i^{15}=i^{12}\times i^{2}\times i=(i^{4})^{3}\times i^{2}\times i=(1)^{3}\times-1\times i=1\times-1\times i=-i$