Chapter 9: Q. 19 (page 630)

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

Short Answer

Expert verified

We get:

$z \cdot w = c o s 130^{\circ} + isin 130^{\circ} \frac{z}{w} = \cos 30^{\circ} + i \sin 30^{\circ}$

Step by step solution

Step 1. Given information

We have been given:

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

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

$\begin{aligned} Z_{1} Z_{2} = r_{1} r_{2} [\cos (θ_{1} + θ_{2}) + i \sin (θ_{1} + θ_{2})] \\ \frac{Z_{1}}{Z_{2}} = \frac{r_{1}}{r_{2}} [\cos (θ_{1} - θ_{2}) + i \sin (θ_{1} - θ_{2})] \end{aligned}$

Step 3. Find zw.

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

Step 4. Find zw.

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

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

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

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

Probability and Statistics

Calculus

Mechanics Maths

Applied Mathematics

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

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