Answer
$-i$
Work Step by Step
The given expression, $
i^{39}
,$ is equivalent to
\begin{array}{l}\require{cancel}
i^{38}\cdot i
\\\\=
(i^{2})^{19}\cdot i
.\end{array}
Using $i^2=-1,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(-1)^{19}\cdot i
\\\\=
(-1)\cdot i
\\\\=
-i
.\end{array}
