Chapter 9: Q. 34 (page 592)

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

Short Answer

Expert verified

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

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

Step by step solution

Step 1 Given that,

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

First find $z w$ .

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

Step 2 Next find zw.

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

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

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=cos120∘+isin120∘w=cos100∘+isin100∘

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

Geometry

Pure Maths

Mechanics Maths

Statistics

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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