Answer
The required operation in polar form is $ z=32\left( \cos 50{}^\circ +i\sin 50{}^\circ \right)$.
Work Step by Step
As
${{\left\{ 2\left( \cos 10{}^\circ +i\sin 10{}^\circ \right) \right\}}^{5}}$
So,
$\begin{align}
& {{\left\{ 2\left( \cos 10{}^\circ +i\sin 10{}^\circ \right) \right\}}^{5}}={{\left( 2 \right)}^{5}}\left( \cos \left( 5\cdot 10{}^\circ \right)+i\sin \left( 5\cdot 10{}^\circ \right) \right) \\
& =32\left( \cos \left( \left( 50{}^\circ \right) \right)+i\sin \left( 50{}^\circ \right) \right) \\
& =32\left( \cos 50{}^\circ +i\sin 50{}^\circ \right)
\end{align}$
So, $ z=32\left( \cos 50{}^\circ +i\sin 50{}^\circ \right)$
Therefore, the required operation in polar form is $ z=32\left( \cos 50{}^\circ +i\sin 50{}^\circ \right)$.
