/*! 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} Q1P Show that if the line through th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q1P (page 77)

Show that if the line through the origin and the point z is rotated 90掳about the origin, it becomes the line through the origin and the point iz. This fact is sometimes expressed by saying that multiplying a complex number byrotates it through90掳. Use this idea in the following problem. Letz=aei蝇tbe the displacement of a particle from the origin at time t. Show that the particle travels in a circle of radius a at velocity v=a蝇and with acceleration of magnitude directed toward the centrev2/aof the circle.

Short Answer

Expert verified

It has been proved.

v=a蝇A=a蝇2

Step by step solution

01

Given Information.

The given expression is, z=aei蝇t.

02

Meaning of rectangular form.

Represent the complex number in rectangular form means writing the given complex number in the form of x + iy in which x is the real part and y is the imaginary part.

03

Change the angle and find equation.

Consider z=ei胃

Change the angle by adding 蟺2.

胃2=胃+蟺2

Find the new number.

z=rei胃2z=re胃+蟺/2iz=re胃i.e蟺i/2z=re胃icos蟺/2+isin蟺/2z=rie胃iz=zi

04

Find the velocity.

Differentiate the equation with respect to time to find the velocity.

v=dzdtv=ddtaei蝇tv=ai蝇ei蝇tv=蝇iaei蝇tv=蝇iz

Find the magnitude.

v=蝇izv=蝇i.zv=蝇a

05

Find the acceleration.

Differentiate the velocity with respect to time to find the acceleration.

v=dzdtv=ddt蝇iaexpi蝇tv=-a蝇2expi蝇tv=蝇2aexpi蝇tv=蝇2i

Find the magnitude.

A=蝇2izA=蝇i.zA=蝇2a

Therefore, it has been proved.

v=a蝇A=a蝇2

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.

5-2i5+2i.

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

(x+iy)3=-1

Show from the power series (8.1) that ez1路ez2=ez1+z2.

For each of the following numbers, first visualize where it is in the complex plane. With a little practice, you can quickly find x,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.

7(cos110掳-isin110掳).

Question:First simplify each of the following numbers to the x+iyform or to therei胃form. Then plot the number in the complex plane.

(1.7-3.2i)2 .
See all solutions

Recommended explanations on Physics Textbooks

Further Mechanics and Thermal Physics

Read Explanation

Astrophysics

Read Explanation

Geometrical and Physical Optics

Read Explanation

Radiation

Read Explanation

Energy Physics

Read Explanation

Thermodynamics

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.