Q. 20 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. 20 (page 630)

Find $z w$ and $\frac{z}{w}$ . Leave your answers in polar form.
$z = 3 (\cos \frac{9 蟺}{5} + i \sin \frac{9 蟺}{5}) w = 2 (\cos \frac{蟺}{5} + i \sin \frac{蟺}{5})$

Short Answer

Expert verified

We get:

$z 鈰� w = 6 [c o s 2 蟺 + isin 2 蟺] \frac{z}{w} = \frac{3}{2} 鈰� (\cos \frac{8 蟺}{5} + isin \frac{8 蟺}{5})$

Step by step solution

Step 1. Given information

We have been given:

$z = 3 (\cos \frac{9 蟺}{5} + i \sin \frac{9 蟺}{5}) w = 2 (\cos \frac{蟺}{5} + i \sin \frac{蟺}{5})$

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.

$z 鈰� w = 3 (c o s \frac{9 蟺}{5} + isin \frac{9 蟺}{5}) 鈰� 2 (c o s \frac{蟺}{5} + isin \frac{蟺}{5}) z 鈰� w = 6 (c o s (\frac{9 蟺}{5} + \frac{蟺}{5}) + isin (\frac{9 蟺}{5} + \frac{蟺}{5})) z 鈰� w = 6 (c o s 2 蟺 + isin 2 蟺)$

Step 4. Find zw.

$\frac{z}{w} = \frac{3 (c o s \frac{9 蟺}{5} + isin \frac{9 蟺}{5})}{2 (c o s \frac{蟺}{5} + isin \frac{蟺}{5})} = \frac{3}{2} 鈰� [\cos (\frac{9 蟺}{5} 鈭� \frac{蟺}{5}) + i \sin (\frac{9 蟺}{5} 鈭� \frac{蟺}{5})] = \frac{3}{2} 鈰� (\cos \frac{8 蟺}{5} + isin \frac{8 蟺}{5})$

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91影视

Find $z w$ and $\frac{z}{w}$ . Leave your answers in polar form.
$z = 3 (\cos \frac{9 蟺}{5} + i \sin \frac{9 蟺}{5}) w = 2 (\cos \frac{蟺}{5} + i \sin \frac{蟺}{5})$

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=3cos9蟺5+isin9蟺5w=2cos蟺5+isin蟺5

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

Logic and Functions

Probability and Statistics

Calculus

Decision Maths

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

Find $z w$ and $\frac{z}{w}$ . Leave your answers in polar form.
$z = 3 (\cos \frac{9 蟺}{5} + i \sin \frac{9 蟺}{5}) w = 2 (\cos \frac{蟺}{5} + i \sin \frac{蟺}{5})$