Answer
The rectangular form of the given complex number is $-18.2-8.5i$.
Work Step by Step
Consider any complex number, given by $z=x+iy$; for a complex number in rectangular form,
$z=x+iy$ ...... (1)
The polar form is given by,
$z=r\left( \cos \theta +i\sin \theta \right)$ …… (2)
Here, $x=r\cos \theta \ \text{ and }\ y=r\sin \theta $,
Divide the value of y by x, to get,
$\tan \theta =\frac{y}{x}$
Also, the value of r is called as moduli of the complex number, given by,
$r=\sqrt{{{x}^{2}}+{{y}^{2}}}$
For any complex number in polar form, $z=r\left( \cos \theta +i\sin \theta \right)$, the rectangular form is,
Using (1) and (2),
$\begin{align}
& z=20\left( \cos 205{}^\circ +i\sin 205{}^\circ \right) \\
& z=x+iy \\
\end{align}$
Simplify it further to get,
$\begin{align}
& 20\left( \cos 205{}^\circ +i\sin 205{}^\circ \right)=20\cos 205{}^\circ +20i\sin 205{}^\circ \\
& =\left( 20\times -0.91 \right)+i\left( 20\times -0.42 \right) \\
& =-18.2-8.5i \\
& 20\left( \cos 205{}^\circ +i\sin 205{}^\circ \right)=-18.2-8.5i
\end{align}$
The rectangular form of the complex number is $-18.2-8.5i$.
