Answer
The rectangular form of the complex number is $3\sqrt{3}+3i$.
Work Step by Step
Here
$\begin{align}
& z=6\left( \cos 30{}^\circ +i\sin 30{}^\circ \right) \\
& =x+iy
\end{align}$
Therefore, $x=6\cos 30{}^\circ,y=6\sin 30{}^\circ $
Simplifying it further, to get,
$\begin{align}
& x=6\times \left( \frac{\sqrt{3}}{2} \right) \\
& =3\sqrt{3} \\
& y=6\times \left( \frac{1}{2} \right) \\
& =3
\end{align}$
So, the rectangular form of the complex number is $3\sqrt{3}+3i$
