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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 9: Q. 34 (page 592)

In Problems $33 - 40$ , find $z w$ and $\frac{z}{w}$ .Leave your answers in polar form.
$z = \cos 120^{鈭�} + i \sin 120^{鈭�} w = \cos 100^{鈭�} + i \sin 100^{鈭�}$

Short Answer

Expert verified

The polar form of $z w$ is, $\cos 220^{鈭�} + i \sin 220^{鈭�}$ .

The polar form of $\frac{z}{w}$ is, $\cos 20^{鈭�} + i \sin 20^{鈭�}$ .

Step by step solution

01

Step 1 Given that,

$z = \cos 120^{鈭�} + i \sin 120^{鈭�} w = \cos 100^{鈭�} + i \sin 100^{鈭�}$

First find $z w$ .

$z . w = (\cos 120^{鈭�} + i \sin 120^{鈭�}) . (\cos 100^{鈭�} + i \sin 100^{鈭�}) = \cos (120^{鈭�} + 100^{鈭�}) + i \sin (120^{鈭�} + 100^{鈭�}) = \cos 220^{鈭�} + i \sin 220^{鈭�}$

02

Step 2 Next find zw.

$\frac{z}{w} = \frac{\cos 120^{鈭�} + i \sin 120^{鈭�}}{\cos 100^{鈭�} + i \sin 100^{鈭�}} = \cos (120^{鈭�} - 100^{鈭�}) + i \sin (120^{鈭�} - 100^{鈭�}) = \cos 20^{鈭�} + i \sin 20^{鈭�}$

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Most popular questions from this chapter

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