Answer
$i$
Work Step by Step
Using $i^2=-1$ and the laws of exponents, the given expression $
i^{1001}
,$ is equivalent to
\begin{array}{l}\require{cancel}
i^{1000}\cdot i
\\\\=
(i^{2})^{500}\cdot i
\\\\=
(-1)^{500}\cdot i
\\\\=
(1)\cdot i
\\\\=
i
.\end{array}