## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 6 - Section 6.5 - Complex Numbers in Polar Form; DeMoivre's Theorem - Exercise Set - Page 767: 28

#### Answer

The rectangular form of the complex number is $6+6\sqrt{3}i$.

#### Work Step by Step

Here \begin{align} & z=12\left( \cos 60{}^\circ +i\sin 60{}^\circ \right) \\ & =x+iy \end{align} Therefore, $x=12\cos 60{}^\circ,y=12\sin 60{}^\circ$ Simplify it further to get, \begin{align} & x=12\times \left( \frac{1}{2} \right) \\ & =6 \\ & y=12\times \left( \frac{\sqrt{3}}{2} \right) \\ & =6\sqrt{3} \end{align} So, the rectangular form of the complex number is $6+6\sqrt{3}i$

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