Answer
The multiplication of the complex numbers in the polar form is $12\left( \cos \frac{3\pi }{10}+i\sin \frac{3\pi }{10} \right)$.
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,
$\begin{align}
& {{z}_{1}}\times {{z}_{2}}=3\times 4\left( \cos \left( \frac{\pi }{5}+\frac{\pi }{10} \right)+i\sin \left( \frac{\pi }{5}+\frac{\pi }{10} \right) \right) \\
& =12\left( \cos \frac{3\pi }{10}+i\sin \frac{3\pi }{10} \right)
\end{align}$
The multiplication of the complex numbers in the polar form is $12\left( \cos \frac{3\pi }{10}+i\sin \frac{3\pi }{10} \right)$
