/*! 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} Q9P Express the following complex nu... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q9P (page 63)

Express the following complex numbers in the x+iyform. Try to visualize each complex number, using sketches as in the examples if necessary. The first twelve problems you should be able to do in your head (and maybe some of the others鈥攖ry it!) Doing a problem quickly in your head saves time over using a computer. Remember that the point in doing problems like this is to gain skill in manipulating complex expressions, so a good study method is to do the problems by hand and use a computer to check your answers.

9.2e-i蟺/2

Short Answer

Expert verified

The complex number x+iyin form is z=-2iand the graph is shown below:

Step by step solution

01

Given information

The given complex number is2e-i蟺/2.

02

Definition of complex numbers

The numbers that are presented in the form of a+ib, where, a,bare the real numbers and 'i'is an imaginary number called complex numbers.

03

Finding the general formx+iy

Let the given complex number bez=2ei蟺/2.

Polar form of the complex number isz=rcos胃+isin胃.

Compare the given complex number with the above two forms.

r=2胃=-蟺2

The value of x,yis rcos胃,rsin胃respectively.

x=rcos胃y=rsin胃

Put the values of rand胃in the above equations.

x=2cos-蟺2x=0y=2sin-蟺2y=-2

The general form is -2i.

04

Draw the graph of the complex number

The plot of the complex number -2iis shown below by using computer:

Therefore, the general form isz=-2i.

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

Find the absolute value of each of the following using the discussion above. Try to do simple problems like these in your head-it saves time.

(1+2i)3.

Express the following complex numbers in the form. Try to visualize each complex number, using sketches as in the examples if necessary. The first twelve problems you should be able to do in your head (and maybe some of the others鈥攖ry it!) Doing a problem quickly in your head saves time over using a computer. Remember that the point in doing problems like this is to gain skill in manipulating complex expressions, so a good study method is to do the problems by hand and use a computer to check your answers.

19. (1鈭�i)8

Find the absolute value of each of the following using the discussion above. Try to do simple problems like these in your head-it saves time.

3ii-3.

Express the following complex numbers in the x+iyform. Try to visualize each complex number, using sketches as in the examples if necessary. The first twelve problems you should be able to do in your head (and maybe some of the others鈥攖ry it!) Doing a problem quickly in your head saves time over using a computer. Remember that the point in doing problems like this is to gain skill in manipulating complex expressions, so a good study method is to do the problems by hand and use a computer to check your answers.

11. localid="1653075389121" role="math" 2e5i蟺/4

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

Rez=0.

See all solutions

Recommended explanations on Physics Textbooks

Translational Dynamics

Read Explanation

Oscillations

Read Explanation

Engineering Physics

Read Explanation

Dynamics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Conservation of Energy and Momentum

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.