Answer
The division of the complex numbers in the polar form is $\cos 240{}^\circ +i\sin 240{}^\circ $.
Work Step by Step
Here,
$\begin{align}
& {{z}_{1}}=\cos 80{}^\circ +i\sin 80{}^\circ \\
& {{z}_{2}}=\cos 200{}^\circ +i\sin 200{}^\circ \\
\end{align}$
Therefore,
$\begin{align}
& \frac{{{z}_{1}}}{{{z}_{2}}}=\frac{1}{1}\left( \cos \left( 80{}^\circ -200{}^\circ \right)+i\sin \left( 80{}^\circ -200{}^\circ \right) \right) \\
& =1\left( \cos \left( -120 \right){}^\circ +i\sin \left( -120 \right){}^\circ \right) \\
& =\cos 240{}^\circ +i\sin 240{}^\circ
\end{align}$
The division of the complex numbers in the polar form is $\cos 240{}^\circ +i\sin 240{}^\circ $
