Answer
$\dfrac{-1}{3}+\dfrac{i}{3}$
Work Step by Step
Multiplying the numerator and the denominator by $i$, the expression \dfrac{1+i}{-3i}
$ simplifies to
}\\
\begin{array}{l}
\dfrac{1+i}{-3i}
\cdot
\dfrac{i}{i}
\\\\=
\dfrac{i+i^2}{-3i^2}
\\\\=
\dfrac{i+(-1)}{-3(-1)}
\\\\=
\dfrac{-1+i}{3}
\\\\=
\dfrac{-1}{3}+\dfrac{i}{3}
.\end{array}
