# Chapter 6 - Section 6.5 - Complex Numbers in Polar Form; DeMoivre's Theorem - Exercise Set - Page 767: 38

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 $28\left( \cos 40{}^\circ +i\sin 40{}^\circ \right)$

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