Answer
The multiplication of the complex numbers in the polar form is $28\left( \cos 40{}^\circ +i\sin 40{}^\circ \right)$.
Work Step by Step
Here,
$\begin{align}
& {{z}_{1}}=4\left( \cos 15{}^\circ +i\sin 15{}^\circ \right) \\
& {{z}_{2}}=7\left( \cos 25{}^\circ +i\sin 25{}^\circ \right) \\
\end{align}$
Therefore,
$\begin{align}
& {{z}_{1}}\times {{z}_{2}}=7\times 4\left( \cos \left( 15{}^\circ +25{}^\circ \right)+i\sin \left( 15{}^\circ +25{}^\circ \right) \right) \\
& =28\left( \cos 40{}^\circ +i\sin 40{}^\circ \right)
\end{align}$
The multiplication of the complex numbers in the polar form is $28\left( \cos 40{}^\circ +i\sin 40{}^\circ \right)$
