Q. 21 Find zw聽and zw. Leave your answ... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 9: Q. 21 (page 630)

Find $z w$ and $\frac{z}{w}$ . Leave your answers in polar form.
$z = 5 (\cos 10^{鈭�} + i \sin 10^{鈭�}) w = \cos 355^{鈭�} + i \sin 355^{鈭�}$

Short Answer

Expert verified

We get:

$z 鈰� w = 5 (c o s 5^{鈭�} + isin 5^{鈭�}) \frac{z}{w} = 5 (c o s 15^{鈭�} + isin 15^{鈭�})$

Step by step solution

Step 1. Given information

We have been given:

$z = 5 (\cos 10^{鈭�} + i \sin 10^{鈭�}) w = \cos 355^{鈭�} + i \sin 355^{鈭�}$

We have to find $z w$ and $\frac{z}{w}$ .

Step 2. Write the formula for the multiplication division of the complex numbers

$\begin{aligned} Z_{1} Z_{2} = r_{1} r_{2} [\cos (胃_{1} + 胃_{2}) + i \sin (胃_{1} + 胃_{2})] \\ \frac{Z_{1}}{Z_{2}} = \frac{r_{1}}{r_{2}} [\cos (胃_{1} 鈭� 胃_{2}) + i \sin (胃_{1} 鈭� 胃_{2})] \end{aligned}$

Step 3. Find zw.

$z 鈰� w = 5 (\cos 10^{鈭�} + isin 10^{鈭�}) 鈰� (\cos 355^{鈭�} + isin 355^{鈭�}) z 鈰� w = 5 [c o s (10^{鈭�} + 355^{鈭�}) + isin (10^{鈭�} + 355^{鈭�})] = 5 (c o s 365^{鈭�} + isin 365^{鈭�}) = 5 (\cos 5^{鈭�} + i s in 5^{鈭�})$

Step 4. Find zw.

$\frac{z}{w} = \frac{5 (\cos 10^{鈭�} + isin 10^{鈭�})}{(\cos 355^{鈭�} + isin 355^{鈭�})} \frac{z}{w} = 5 [c o s (10^{鈭�} 鈭� 355^{鈭�}) + isin (10^{鈭�} 鈭� 355^{鈭�})] = 5 (c o s (鈭� 345^{鈭�}) + isin (鈭� 345^{鈭�})) = 5 (c o s 345^{鈭�} - isin 345^{鈭�}) = 5 (c o s (380^{o} - 15^{鈭�}) - isin (380^{o} - 15^{鈭�})) = 5 (c o s 15^{鈭�} + i s i n 15^{鈭�})$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Find $z w$ and $\frac{z}{w}$ . Leave your answers in polar form.
$z = 5 (\cos 10^{鈭�} + i \sin 10^{鈭�}) w = \cos 355^{鈭�} + i \sin 355^{鈭�}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the formula for the multiplication division of the complex numbers

Step 3. Find zw.

Step 4. Find zw.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Mechanics Maths

Pure Maths

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

91影视

Find zwand zw. Leave your answers in polar form.z=5cos10鈭�+isin10鈭�w=cos355鈭�+isin355鈭�

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the formula for the multiplication division of the complex numbers

Step 3. Find zw.

Step 4. Find zw.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Mechanics Maths

Pure Maths

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Find $z w$ and $\frac{z}{w}$ . Leave your answers in polar form.
$z = 5 (\cos 10^{鈭�} + i \sin 10^{鈭�}) w = \cos 355^{鈭�} + i \sin 355^{鈭�}$