Answer
The multiplication of the complex numbers in the polar form is $\cos \frac{7\pi }{12}+i\sin \frac{7\pi }{12}$.
Work Step by Step
Here,
$\begin{align}
& {{z}_{1}}=1\left( \cos \frac{\pi }{4}+i\sin \frac{\pi }{4} \right) \\
& {{z}_{2}}=1\left( \cos \frac{\pi }{3}+i\sin \frac{\pi }{3} \right) \\
\end{align}$
Therefore,
$\begin{align}
& {{z}_{1}}\times {{z}_{2}}=1\times 1\left( \cos \left( \frac{\pi }{4}+\frac{\pi }{3} \right)+i\sin \left( \frac{\pi }{4}+\frac{\pi }{3} \right) \right) \\
& =\cos \frac{7\pi }{12}+i\sin \frac{7\pi }{12}
\end{align}$
The multiplication of the complex numbers in the polar form is $\cos \frac{7\pi }{12}+i\sin \frac{7\pi }{12}$
