Answer
The rectangular form of the complex number is $-5\sqrt{3}-5i$.
Work Step by Step
Here
$\begin{align}
& z=10\left( \cos 210{}^\circ +i\sin 210{}^\circ \right) \\
& =x+iy
\end{align}$
Therefore, $x=10\cos 210{}^\circ,y=5\sin 210{}^\circ $
Simplify it further to get,
$\begin{align}
& x=10\times (-\frac{\sqrt{3}}{2}) \\
& =-5\sqrt{3} \\
& y=10\times (-\frac{1}{2}) \\
& =-5
\end{align}$
So, the rectangular form of the complex number is $-5\sqrt{3}-5i$
