Answer
$7+4i$
Work Step by Step
Using the properties of radicals and that $i=\sqrt{-1}$, then the given expression, $
7+\sqrt{-16}
,$ is equivalent to
\begin{array}{l}\require{cancel}
7+\sqrt{-1}\cdot\sqrt{16}
\\\\=
7+i\cdot\sqrt{(4)^2}
\\\\=
7+i\cdot4
\\\\=
7+4i
.\end{array}