Chapter 9: Q. 11 (page 631)

In Problems 10–12, perform the given operation, where $z = 2 (\cos 85 ° + i \sin 85 °)$ and $w = 3 (\cos 22 ° + i \sin 22 °)$ . Write your answer in polar form.
$\frac{w}{z}$

Short Answer

Expert verified

The answer is $\frac{w}{z} = \frac{3}{2} (\cos 297 ° + i \sin 297 °)$

Step by step solution

Step 1. Given information

We have been given $z = 2 (\cos 85 ° + i \sin 85 °)$ and $w = 3 (\cos 22 ° + i \sin 22 °)$ .

We have to perform the operation $\frac{w}{z}$

Step 2. Perform the operation

$\frac{w}{z} = \frac{3 (\cos 22 ° + i \sin 22 °)}{2 (\cos 85 ° + i \sin 85 °)} = \frac{3}{2} [\cos (22 ° - 85 °) + i \sin (22 ° - 85 °)] = \frac{3}{2} (\cos (- 63 °) + i \sin (- 63 °)) = \frac{3}{2} (\cos (360 ° - 63 °) + i \sin (360 ° - 63 °)) = \frac{3}{2} (\cos 297 ° + i \sin 297 °)$

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In Problems 10–12, perform the given operation, where $z = 2 (\cos 85 ° + i \sin 85 °)$ and $w = 3 (\cos 22 ° + i \sin 22 °)$ . Write your answer in polar form.
$\frac{w}{z}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Perform the operation

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In Problems 10–12, perform the given operation, where z=2cos85°+isin85°and w=3cos22°+isin22°. Write your answer in polar form.wz

Short Answer

Step by step solution

Step 1. Given information

Step 2. Perform the operation

One App. One Place for Learning.

Most popular questions from this chapter

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Probability and Statistics

Statistics

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Study anywhere. Anytime. Across all devices.

In Problems 10–12, perform the given operation, where $z = 2 (\cos 85 ° + i \sin 85 °)$ and $w = 3 (\cos 22 ° + i \sin 22 °)$ . Write your answer in polar form.
$\frac{w}{z}$