Q. 19 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. 19 (page 630)

Find $z w$ and $\frac{z}{w}$ . Leave your answers in polar form.
$\begin{aligned} z = \cos 80^{鈭�} + i \sin 80^{鈭�} \\ w = \cos 50^{鈭�} + i \sin 50^{鈭�} \end{aligned}$

Short Answer

Expert verified

We get:

$z 鈰� w = c o s 130^{鈭�} + isin 130^{鈭�} \frac{z}{w} = \cos 30^{鈭�} + i \sin 30^{鈭�}$

Step by step solution

Step 1. Given information

We have been given:

$\begin{aligned} z = \cos 80^{鈭�} + i \sin 80^{鈭�} \\ w = \cos 50^{鈭�} + i \sin 50^{鈭�} \end{aligned}$

We have to find localid="1646900510241" $z w$ 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.

$z 鈰� w = (\cos 80^{鈭�} + i \sin 80^{鈭�}) 鈰� (\cos 50^{鈭�} + i \sin 50^{鈭�}) z 鈰� w = (1 鈰� 1) [c o s (80^{鈭�} + 50^{鈭�}) + isin (80^{鈭�} + 50^{o})] = \cos 130^{鈭�} + i \sin 130^{鈭�}$

Step 4. Find zw.

$\frac{z}{w} = \frac{(\cos 80^{鈭�} + i \sin 80^{鈭�})}{(\cos 50^{鈭�} + i \sin 50^{鈭�})} \frac{z}{w} = c o s (80^{鈭�} 鈭� 50^{鈭�}) + isin (80^{鈭�} 鈭� 50^{鈭�}) = \cos 30^{鈭�} + isin 30^{鈭�}$

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91影视

Find $z w$ and $\frac{z}{w}$ . Leave your answers in polar form.
$\begin{aligned} z = \cos 80^{鈭�} + i \sin 80^{鈭�} \\ w = \cos 50^{鈭�} + i \sin 50^{鈭�} \end{aligned}$

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.

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91影视

Find zwand zw. Leave your answers in polar form.z=cos80鈭�+isin80鈭�w=cos50鈭�+isin50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

Applied Mathematics

Probability and Statistics

Logic and Functions

Pure Maths

Calculus

Study anywhere. Anytime. Across all devices.

Find $z w$ and $\frac{z}{w}$ . Leave your answers in polar form.
$\begin{aligned} z = \cos 80^{鈭�} + i \sin 80^{鈭�} \\ w = \cos 50^{鈭�} + i \sin 50^{鈭�} \end{aligned}$