Chapter 9: Q. 30 (page 592)

In Problems $23 - 32$ , write each complex number in rectangular form.
$0.4 (\cos 200^{\circ} + i \sin 200^{\circ})$ .

Short Answer

Expert verified

The rectangular form of the complex number $0.4 (\cos 200^{\circ} + i \sin 200^{\circ})$ is, $- 0.3758 - 0.1368 i$ .

Step by step solution

Step 1 Given complex number is,

$0.4 (\cos 200^{\circ} + i \sin 200^{\circ})$ .

We can simplify the terms inside the brackets and write it in the rectangular form.

$z = 0.4 (\cos 200^{\circ} + i \sin 200^{\circ}) z = 0.4 (\cos (180^{\circ} + 20^{\circ}) + i \sin (180^{\circ} + 20^{\circ})) z = 0.4 (- \cos 20^{\circ} - i \sin 20^{\circ}) [\cos (180^{\circ} + θ) = - \cos θ \sin (180^{\circ} + θ) = - \sin θ]$

Step 2 Now substitute the values for cos 20∘,sin 20∘.

$z = 0.4 (- 0.9396 - 0.342 i) z = - 0.3758 - 0.1368 i$

Thus the required rectangular form is, $- 0.3758 - 0.1368 i$ .

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In Problems $23 - 32$ , write each complex number in rectangular form.
$0.4 (\cos 200^{\circ} + i \sin 200^{\circ})$ .

Short Answer

Step by step solution

Step 1 Given complex number is,

Step 2 Now substitute the values for cos 20∘,sin 20∘.

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In Problems 23-32, write each complex number in rectangular form.0.4cos200∘+isin200∘.

Short Answer

Step by step solution

Step 1 Given complex number is,

Step 2 Now substitute the values for cos 20∘,sin 20∘.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Applied Mathematics

Probability and Statistics

Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

In Problems $23 - 32$ , write each complex number in rectangular form.
$0.4 (\cos 200^{\circ} + i \sin 200^{\circ})$ .