Chapter 9: Q. 35 (page 592)

In Problems $33 - 40$ , find $z w$ and $\frac{z}{w}$ .Leave your answers in polar form.
$z = 3 (\cos 130^{\circ} + i \sin 130^{\circ}) w = 4 (\cos 270^{\circ} + i \sin 270^{\circ})$

Short Answer

Expert verified

The polar form of $z w$ is, role="math" localid="1646761395771" $12 [\cos 40^{\circ} + i \sin 40^{\circ}]$ .

The polar form of $\frac{z}{w}$ is, $\frac{3}{4} [\cos 220^{\circ} + i \sin 220^{\circ}]$ .

Step by step solution

Step 1 Given that,

$z = 3 (\cos 130^{\circ} + i \sin 130^{\circ}) w = 4 (\cos 270^{\circ} + i \sin 270^{\circ})$

First find $z w$ .

$z . w = 3 (\cos 130^{\circ} + i \sin 130^{\circ}) . 4 (\cos 270^{\circ} + i \sin 270^{\circ}) = 12 [\cos (130^{\circ} + 270^{\circ}) + i \sin (130^{\circ} + 270^{\circ})] = 12 [\cos 400^{\circ} + i \sin 400^{\circ}]$

we know that , $\cos (360^{\circ} + θ) = \cos θ,$ so $\cos (360^{\circ} + 40^{\circ}) = \cos 40^{\circ}$ .

$z . w = 12 [\cos 40^{\circ} + i \sin 40^{\circ}]$ .

Step 2 Next find zw.

$\frac{z}{w} = \frac{3 (\cos 130^{\circ} + i \sin 130^{\circ})}{4 (\cos 270^{\circ} + i \sin 270^{\circ})} = \frac{3}{4} [\cos (130^{\circ} - 270^{\circ}) + i \sin (130^{\circ} - 270^{\circ})] = \frac{3}{4} [\cos (- 140^{\circ}) + i \sin (- 140^{\circ})]$

we know that,

\cos (- 140^{\circ}) = \cos (360^{\circ} - 220^{\circ}) = \cos 220^{\circ}

Thus, $\frac{z}{w} = \frac{3}{4} [\cos 220^{\circ} + i \sin 220^{\circ}]$ .

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In Problems $33 - 40$ , find $z w$ and $\frac{z}{w}$ .Leave your answers in polar form.
$z = 3 (\cos 130^{\circ} + i \sin 130^{\circ}) w = 4 (\cos 270^{\circ} + i \sin 270^{\circ})$

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=3cos130∘+isin130∘w=4cos270∘+isin270∘

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

Logic and Functions

Probability and Statistics

Geometry

Statistics

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problems $33 - 40$ , find $z w$ and $\frac{z}{w}$ .Leave your answers in polar form.
$z = 3 (\cos 130^{\circ} + i \sin 130^{\circ}) w = 4 (\cos 270^{\circ} + i \sin 270^{\circ})$