/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q53P Describe geometrically the set o... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q53P (page 54)

Describe geometrically the set of points in the complex plane satisfying the following equations.

|z-1|=1.

Short Answer

Expert verified

This is the equation of the circle with a center 1,0and radius r=1.

Step by step solution

01

Given Information

The equation is Z-1=1.

02

Definition of the Complex number

A complex number can be written as:


z=x+iy

Where z is the complex number, x and y are real numbers, and i is known as iota, whose value is-1.

The modulus of a complex number can be calculated as:

|Z|=x2+y2

03

Find the value

The equation is Z-1=1.

The complex number is role="math" localid="1658466205357" z=x+yi.

role="math" localid="1658466195116" x+yi-1=1

Solve further:

(x-1)2+y2=1(x-1)2+y2=1

Hence, this is the equation of circle with a center 1,0and radius r=1.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Question: Describe geometrically the set of points in the complex plane satisfying the following equations.

z2=-z炉2..

Use Problems 27 and 28 to find the following absolute values. If you understand Problems 27 and 28 and equation (5.1), you should be able to do these in your head.

|e颈蟺1+i|

Solve for all possible values of the real numbers x and y in the following equations.

(x+iy)3=-1

For each of the following numbers, first visualize where it is in the complex plane. With a little practice you can quickly findx,y,r,胃 in your head for these simple problems. Then plot the number and label it in five ways as in Figure 3.3. Also plot the complex conjugate of the number.

5(cos20掳+isin20掳).

For each of the following numbers, first visualize where it is in the complex plane. With a little practice you can quickly findx,y,r,胃in your head for these simple problems. Then plot the number and label it in five ways as in Figure 3.3. Also plot the complex conjugate of the number.

(cos蟺-isin蟺).
See all solutions

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

Read Explanation

Electricity and Magnetism

Read Explanation

Medical Physics

Read Explanation

Engineering Physics

Read Explanation

Famous Physicists

Read Explanation

Mechanics and Materials

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.