## Precalculus (6th Edition) Blitzer

The rectangular form of the complex number is $-5\sqrt{3}-5i$.
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 $-5\sqrt{3}-5i$