Answer
The rectangular form of the complex number is $-2-2\sqrt{3}i$.
Work Step by Step
Here
$\begin{align}
& z=4\left( \cos 240{}^\circ +i\sin 240{}^\circ \right) \\
& =x+iy
\end{align}$
Therefore, $x=4\cos 240{}^\circ,y=4\sin 240{}^\circ $
Simplify it further to get,
$\begin{align}
& x=4\times \left( -\frac{1}{2} \right) \\
& =-2 \\
& y=4\times \left( -\frac{\sqrt{3}}{2} \right) \\
& =-2\sqrt{3}
\end{align}$
So, the rectangular form of the complex number is $-2-2\sqrt{3}i$
