Q. 38 In Problems 33-40, find zw聽and ... [FREE SOLUTION]

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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. 38 (page 592)

In Problems $33 - 40$ , find $z w$ and $\frac{z}{w}$ .Leave your answers in polar form.
$z = 4 (\cos \frac{3 蟺}{8} + i \sin \frac{3 蟺}{8}) w = 2 (\cos \frac{9 蟺}{16} + i \sin \frac{9 蟺}{16})$

Short Answer

Expert verified

The polar form of $z w$ is, $8 (\cos \frac{15 蟺}{16} + i \sin \frac{15 蟺}{16})$ .

The polar form of $\frac{z}{w}$ is, $2 (\cos \frac{3 蟺}{16} - i \sin \frac{3 蟺}{16})$ .

Step by step solution

Step 1 Given that,

$z = 4 (\cos \frac{3 蟺}{8} + i \sin \frac{3 蟺}{8}) w = 2 (\cos \frac{9 蟺}{16} + i \sin \frac{9 蟺}{16})$

First find $z w$ .

$z . w = 4 (\cos \frac{3 蟺}{8} + i \sin \frac{3 蟺}{8}) . 2 (\cos \frac{9 蟺}{16} + i \sin \frac{9 蟺}{16}) = 8 (\cos (\frac{3 蟺}{8} + \frac{9 蟺}{16}) + i \sin (\frac{3 蟺}{8} + \frac{9 蟺}{16})) = 8 (\cos (\frac{6 蟺 + 9 蟺}{16}) + i \sin (\frac{6 蟺 + 9 蟺}{16})) = 8 (\cos \frac{15 蟺}{16} + i \sin \frac{15 蟺}{16})$

Step 2 Next find zw.

$\frac{z}{w} = \frac{4 (\cos \frac{3 蟺}{8} + i \sin \frac{3 蟺}{8})}{2 (\cos \frac{9 蟺}{16} + i \sin \frac{9 蟺}{16})} = 2 [\cos (\frac{3 蟺}{8} - \frac{9 蟺}{16}) + i \sin (\frac{3 蟺}{8} - \frac{9 蟺}{16})] = 2 [\cos (\frac{6 蟺 - 9 蟺}{16}) + i \sin (\frac{6 蟺 - 9 蟺}{16})] = 2 [\cos (\frac{- 3 蟺}{16}) + i \sin (\frac{- 3 蟺}{16})]$

We know that,

\cos (- 胃) = \cos 胃 \sin (- 胃) = - \sin 胃

Thus,

$\frac{z}{w} = 2 [\cos (\frac{3 蟺}{16}) - i \sin (\frac{3 蟺}{16})]$

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91影视

In Problems $33 - 40$ , find $z w$ and $\frac{z}{w}$ .Leave your answers in polar form.
$z = 4 (\cos \frac{3 蟺}{8} + i \sin \frac{3 蟺}{8}) w = 2 (\cos \frac{9 蟺}{16} + i \sin \frac{9 蟺}{16})$

Short Answer

Step by step solution

Step 1 Given that,

Step 2 Next find zw.

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91影视

In Problems 33-40, find zwand zw.Leave your answers in polar form.z=4cos3蟺8+isin3蟺8w=2cos9蟺16+isin9蟺16

Short Answer

Step by step solution

Step 1 Given that,

Step 2 Next find zw.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Mechanics Maths

Geometry

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problems $33 - 40$ , find $z w$ and $\frac{z}{w}$ .Leave your answers in polar form.
$z = 4 (\cos \frac{3 蟺}{8} + i \sin \frac{3 蟺}{8}) w = 2 (\cos \frac{9 蟺}{16} + i \sin \frac{9 蟺}{16})$