Chapter 9: Q. 14 (page 630)

Write each complex number in polar form. Express each argument in degrees.
$- 1 - i$

Short Answer

Expert verified

The polar form of $z = - 1 - i$ is $\sqrt{2} (\cos 225^{o} + i \sin 225^{o})$

Step by step solution

Step 1. Given data

$z = - 1 - i$

Step 2. Calculate the distance r

The polar form of $z = x + i y$ is $z = r (\cos θ + i \sin θ)$

We know,

$|z| = r = \sqrt{x^{2} + y^{2}}$

Substituting the values of (x, y)=(-1, -1),

$r = \sqrt{{(- 1)}^{2} + {(- 1)}^{2}}$

$r = \sqrt{2}$

Step 3. Calculating the value of θ

Substitute $x = r \cos θ$ and $y = r \sin θ$ ,

Therefore, $\sin θ = \frac{y}{r} = \frac{- 1}{\sqrt{2}}$ and

$\cos θ = \frac{x}{r} = \frac{- 1}{\sqrt{2}}$

since, $\sin 225^{o} = \frac{- 1}{\sqrt{2}}$ and $\cos 225^{o} = \frac{- 1}{\sqrt{2}}$

Therefore, $θ = 225^{o}$

Therefore, the polar form of $z = - 1 - i$ is $\sqrt{2} (\cos 225^{0} + i \sin 225^{0})$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Write each complex number in polar form. Express each argument in degrees.
$- 1 - i$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Calculate the distance r

Step 3. Calculating the value of θ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Pure Maths

Statistics

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Write each complex number in polar form. Express each argument in degrees.-1-i

Short Answer

Step by step solution

Step 1. Given data

Step 2. Calculate the distance r

Step 3. Calculating the value of θ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Pure Maths

Statistics

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Write each complex number in polar form. Express each argument in degrees.
$- 1 - i$