Answer
The rectangular form of $z=0.6\left( \cos 100{}^\circ +i\sin 100{}^\circ \right)$ is $z\approx \left( -0.1+0.6i \right)$.
Work Step by Step
The rectangular form of a complex number is $z=a+ib$, where $a$ and $b$ are rectangular coordinates. In the polar form the complex number $z=a+ib$ is represented as $z=r\left( \cos \theta +i\sin \theta \right)$, where r is the distance of the complex number from the origin and $\theta $ is the respective angle.
Here, the given complex number is in the polar form with $r=0.6$ and $\theta =100{}^\circ $.
Since, $\cos 100{}^\circ \approx -\ 0.17\ \text{ and }\ \sin 100{}^\circ =0.98$
Therefore,
$\begin{align}
& z=0.6\left( \cos 100{}^\circ +i\sin 100{}^\circ \right) \\
& \approx 0.6\left( -0.17+i0.98 \right) \\
& \approx \left( \left( -0.17 \right)\left( 0.6 \right)+i\left( 0.98 \right)\left( 0.6 \right) \right) \\
& \approx \left( -0.102+0.588i \right)
\end{align}$
$\approx \left( -0.1+0.6i \right)$
