Chapter 9: Q. 12 (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.
$w^{5}$

Short Answer

Expert verified

The answer is $243 (\cos 110 ° + i \sin 110 °)$

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 $w^{5}$

Step 2. Perform the operation

$w^{5} = 3^{5} (\cos (5 \times 22 °) + i \sin (5 \times 22 °)) = 243 (\cos 110 ° + i \sin 110 °)$

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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.
$w^{5}$

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.w5

Short Answer

Step by step solution

Step 1. Given information

Step 2. Perform the operation

One App. One Place for Learning.

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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.
$w^{5}$