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Notes to teachers and students:

When we teach complex numbers to beginning engineering students, we encourage a geometrical picture supported by an algebraic structure . Every algebraic manipulation carried out in a lecture is accompanied by a care-fully drawn picture in order to fix the idea that geometry and algebra gohand-in-glove to complete our understanding of complex numbers. We assign essentially every problem for homework.

We use the MATLAB programs in this chapter to illustrate the theory of complex numbers and to develop skill with the MATLAB language. The numerical experiment introduces students to the basic quadratic equation of electrical and computer engineering and shows how the roots ofthis quadratic equation depend on the coefficients of the equation.

“Representing Complex Numbers in a Vector Space,” is a little demanding for freshmen but easily accessible to sophomores. It may becovered for additional insight, skipped without consequence, or covered after Chapter 4 . “An Electric Field Computation,” is well beyond most freshmen, and it is demanding for sophomores. Nonetheless, an expertin electromagnetics might want to cover the section "An electric Field Computation" for the insight it brings to the use of complex numbers for representing two-dimensional real quantities.

Introduction

It is hard to overestimate the value of complex numbers. They first arose in the study of roots for quadratic equations. But, as with so manyother great discoveries, complex numbers have found widespread application well outside their original domain of discovery. They are now used throughoutmathematics, applied science, and engineering to represent the harmonic nature of vibrating systems and oscillating fields. For example, complex numbers may be used to study

  1. traveling waves on a sea surface;
  2. standing waves on a violin string;
  3. the pure tone of a Kurzweil piano;
  4. the acoustic field in a concert hall;
  5. the light of a He-Ne laser;
  6. the electromagnetic field in a light show;
  7. the vibrations in a robot arm;
  8. the oscillations of a suspension system;
  9. the carrier signal used to transmit AM or FM radio;
  10. the carrier signal used to transmit digital data over telephone lines; and
  11. the 60 Hz signal used to deliver power to a home.

In this chapter we develop the algebra and geometry of complex numbers. In Chapter 3 we will show how complex numbers are used to build phasor representations of power and communication signals.

Questions & Answers

how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, A first course in electrical and computer engineering. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col10685/1.2
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