Answer
The division of the complex numbers in the polar form is $\frac{3}{10}\left( \cos \frac{31\pi }{144}+i\sin \frac{31\pi }{144} \right)$.
Work Step by Step
Here,
$\begin{align}
& {{z}_{1}}=3\left( \cos \frac{5\pi }{18}+i\sin \frac{5\pi }{18} \right) \\
& {{z}_{2}}=10\left( \cos \frac{\pi }{16}+i\sin \frac{\pi }{16} \right) \\
\end{align}$
Therefore,
$\begin{align}
& \frac{{{z}_{1}}}{{{z}_{2}}}=\frac{3}{10}\left( \cos \left( \frac{5\pi }{18}-\frac{\pi }{16} \right)+i\sin \left( \frac{5\pi }{18}-\frac{\pi }{16} \right) \right) \\
& =\frac{3}{10}\left( \cos \frac{31\pi }{144}+i\sin \frac{31\pi }{144} \right)
\end{align}$
The division of the complex numbers in the polar form is $\frac{3}{10}\left( \cos \frac{31\pi }{144}+i\sin \frac{31\pi }{144} \right)$
