Chapter 9: Q. 37 (page 592)

In Problems $33 - 40$ , find $z w$ and $\frac{z}{w}$ .Leave your answers in polar form.
$z = 2 (\cos \frac{π}{8} + i \sin \frac{π}{8}) w = 2 (\cos \frac{π}{10} + i \sin \frac{π}{10})$

Short Answer

Expert verified

The polar form of $z w$ is, $4 (\cos \frac{9 π}{40} + i \sin \frac{9 π}{40})$ .

The polar form of $\frac{z}{w}$ is, $\cos \frac{π}{40} + i \sin \frac{π}{40}$

Step by step solution

Step 1 Given that,

$z = 2 (\cos \frac{π}{8} + i \sin \frac{π}{8}) w = 2 (\cos \frac{π}{10} + i \sin \frac{π}{10})$

First find $z w$ .

$z . w = 2 (\cos \frac{π}{8} + i \sin \frac{π}{8}) . 2 (\cos \frac{π}{10} + i \sin \frac{π}{10}) = 4 (\cos (\frac{π}{8} + \frac{π}{10}) + i \sin (\frac{π}{8} + \frac{π}{10})) = 4 (\cos (\frac{5 π + 4 π}{40}) + i \sin (\frac{5 π + 4 π}{40})) = 4 (\cos \frac{9 π}{40} + i \sin \frac{9 π}{40})$

Step 2 Next find zw.

$\frac{z}{w} = \frac{2 (\cos \frac{π}{8} + i \sin \frac{π}{8})}{2 (\cos \frac{π}{10} + i \sin \frac{π}{10})} = \cos (\frac{π}{8} - \frac{π}{10}) + i \sin (\frac{π}{8} - \frac{π}{10}) = \cos (\frac{5 π - 4 π}{40}) + i \sin (\frac{5 π - 4 π}{40}) = \cos (\frac{π}{40}) + i \sin (\frac{π}{40})$

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In Problems $33 - 40$ , find $z w$ and $\frac{z}{w}$ .Leave your answers in polar form.
$z = 2 (\cos \frac{π}{8} + i \sin \frac{π}{8}) w = 2 (\cos \frac{π}{10} + i \sin \frac{π}{10})$

Short Answer

Step by step solution

Step 1 Given that,

Step 2 Next find zw.

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In Problems 33-40, find zwand zw.Leave your answers in polar form.z=2cosπ8+isinπ8w=2cosπ10+isinπ10

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

Probability and Statistics

Calculus

Geometry

Theoretical and Mathematical Physics

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems $33 - 40$ , find $z w$ and $\frac{z}{w}$ .Leave your answers in polar form.
$z = 2 (\cos \frac{π}{8} + i \sin \frac{π}{8}) w = 2 (\cos \frac{π}{10} + i \sin \frac{π}{10})$