# Chapter 6 - Test - Page 800: 13

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 $z=32\left( \cos 50{}^\circ +i\sin 50{}^\circ \right)$.

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