Answer
The division of the complex numbers in the polar form is $\frac{3}{4}\left( \cos \frac{\pi }{10}+i\sin \frac{\pi }{10} \right)$.
Work Step by Step
Here,
$\begin{align}
& {{z}_{1}}=3\left( \cos \frac{\pi }{5}+i\sin \frac{\pi }{5} \right) \\
& {{z}_{2}}=4\left( \cos \frac{\pi }{10}+i\sin \frac{\pi }{10} \right) \\
\end{align}$
Therefore
$\begin{align}
& \frac{{{z}_{1}}}{{{z}_{2}}}=\frac{3}{4}\left( \cos \left( \frac{\pi }{5}-\frac{\pi }{10} \right)+i\sin \left( \frac{\pi }{5}-\frac{\pi }{10} \right) \right) \\
& =\frac{3}{4}\left( \cos \frac{\pi }{10}+i\sin \frac{\pi }{10} \right)
\end{align}$
The division of the complex numbers in the polar form is $\frac{3}{4}\left( \cos \frac{\pi }{10}+i\sin \frac{\pi }{10} \right)$
