Answer
The required operation in polar form is $ z=50\left( \cos 20{}^\circ +i\sin 20{}^\circ \right)$
Work Step by Step
Consider the given expression $5\left( \cos 15{}^\circ +i\sin 15{}^\circ \right)\cdot 10\left( \cos 5{}^\circ +i\sin 5{}^\circ \right)$
So, $\begin{align}
& 5\left( \cos 15{}^\circ +i\sin 15{}^\circ \right)\cdot 10\left( \cos 5{}^\circ +i\sin 5{}^\circ \right)=\left( 5\cdot 10 \right)\left( \cos \left( 15{}^\circ +5{}^\circ \right)+i\sin \left( 15{}^\circ +5{}^\circ \right) \right) \\
& =50\left( \cos 20{}^\circ +i\sin 20{}^\circ \right)
\end{align}$
So, $ z=50\left( \cos 20{}^\circ +i\sin 20{}^\circ \right)$
Therefore, the required operation in polar form is $ z=50\left( \cos 20{}^\circ +i\sin 20{}^\circ \right)$.
