Answer
$-2$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To divide the given expression, $
\dfrac{3+i}{i}
,$ multiply both the numerator and the denominator by $i$. Use $i^2=-1.$
$\bf{\text{Solution Details:}}$
Multiplying both the numerator and the denominator by $i,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{3+i}{i}\cdot\dfrac{i}{i}
\\\\=
\dfrac{(3+i)i}{i^2}
.\end{array}
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{(3)i+(i)i}{i^2}
\\\\=
\dfrac{3+i^2}{i^2}
.\end{array}
Since $i^2=-1,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{3+(-1)}{-1}
\\\\=
\dfrac{2}{-1}
\\\\=
-2
.\end{array}
