Chapter 9: Q. 21 (page 630)

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

Short Answer

Expert verified

We get:

$z \cdot w = 5 (c o s 5^{\circ} + isin 5^{\circ}) \frac{z}{w} = 5 (c o s 15^{\circ} + isin 15^{\circ})$

Step by step solution

Step 1. Given information

We have been given:

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

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

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

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

Step 3. Find zw.

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

Step 4. Find zw.

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

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

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=5cos10∘+isin10∘w=cos355∘+isin355∘

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

Applied Mathematics

Probability and Statistics

Pure Maths

Logic and Functions

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

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