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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. 33 (page 592)

In Problems $33 - 40$ , find $z w$ and $\frac{z}{w}$ .Leave your answers in polar form.
$z = 2 (\cos 40^{鈭�} + i \sin 40^{鈭�}) w = 4 (\cos 20^{鈭�} + i \sin 20^{鈭�})$

Short Answer

Expert verified

The polar form of $z w$ is, $8 [\cos 60^{鈭�} + i \sin 60^{鈭�}]$

The polar form of $\frac{z}{w}$ is, $\frac{1}{2} [\cos 20^{鈭�} + i \sin 20^{鈭�}]$ .

Step by step solution

01

Step 1 Given that,

$z = 2 (\cos 40^{鈭�} + i \sin 40^{鈭�}) w = 4 (\cos 20^{鈭�} + i \sin 20^{鈭�})$

First find $z w$ .

$z . w = 2 (\cos 40^{鈭�} + i \sin 40^{鈭�}) . 4 (\cos 20^{鈭�} + i \sin 20^{鈭�}) = 8 [\cos (40^{鈭�} + 20^{鈭�}) + i \sin (40^{鈭�} + 20^{鈭�})] = 8 [\cos 60^{鈭�} + i \sin 60^{鈭�}]$

02

Step 2 Next find zw.

$\frac{z}{w} = \frac{2 (\cos 40^{鈭�} + i \sin 40^{鈭�})}{4 (\cos 20^{鈭�} + i \sin 20^{鈭�})} = \frac{1}{2} [\cos (40^{鈭�} - 20^{鈭�}) + i \sin (40^{鈭�} - 20^{鈭�})] = \frac{1}{2} [\cos 20^{鈭�} + i \sin 20^{鈭�}]$

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Most popular questions from this chapter

Use the vectors in the figure at the right to graph each of the following vectors.

$u - v$

Identify and graph each polar equation. Verify your graph using a graphing utility.

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find the unit vector in the same direction as $v$

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In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.

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$(6.3, 3.8)$

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