Concept of Complex Number ...

[sanaullah2015]

Hellow

My question is about Complex number.
I can solve and calculate complex numbers. But i m still Unsure about the Concept of Complex number.
I have read many articles and they say that a symbol i is added to make the solutions possible.\

In communication engineering, as well as Electrical engineering, this number plays an important role.

Keeping this in mind, Tell me what does the real part and imaginary part of a Complex number shows with an example..Take capacitor or Inductor.
We have learned in primary classes about the Numbers with Fundamental Concepts.
Tell me the Fundamental Idea and Concept of Complex number in context to any application or Example so that the idea behind the number can be visualized properly.

We talk a lot about impedance in transmission lines and they all are in complex number,even in Electrical Machines, Transformer or Motors, I dont understand where actually the real and imaginary part lie??? What does the Real part in practical as well as the imaginary part shows??
Can you Evaluate or Mark and show me from some observation ( or from graph ,a point ) practically and name it complex number with real and imaginory?

Saying so , Please share links,Flash Demonstration, so that i can easily understand this number fundamentally!

And why the real part and imaginoary part are added?? to combine a new number,? and how?
Justify with REASONS AND EXPLANATION
And since symbol "i" is imaginary , how one can translate the word imaginary?Even knowing the complex number hold a significant value in engineering?Does "i" have some transformation?
Thanks

Regards

 

[Mad I.D.]

Hi.

Think about this. If all the numbers were real, how would you describe phase shift in electrical circuits? With complex numbers because they have magnitude and phase!

E.q. when you connect a voltage to a capacitor, the current will not be V/real(Z), it will be V/Z where Z is a complex number. That's why impedance of a capacitor is NOT REAL !! It's imaginary. It has a "j". And the "j" means that component will influence the phase somehow! Resistors have pure real impedance, and we know resistors can't effect the phase.

Think about complex numbers as a mathematical tool which we engineers use to describe electrical circuits.

Good luck with your studies.

 

[Prototyp_V1.0]

Here is one thaught to think at:
An imaginary number can be represented as a vector in a Re/Im plane (same as X/Y plane).

Imagine a sine wave. The same imaginary number can be represented as a difference in phase angle and amplitude (when imaginary number is represented by polar coordinates.

That's why you can use imaginary numbers to calculate voltage out from a voltage divider consisting of impedances rather than resistors.

Pictures attached describe an imaginary number as a vector and as a sinous curve.

 

[NineTailedDemonFox]

^^+1

The graph above makes it clear how you represent the real and imaginary parts

Adding to the comments made above, when I was a novice in electrical concepts and strong in math, I tried to understand this concept mathematically.

For example, consider an AC voltage signal (signal A) of amplitude 50 at 30 degrees phase shift to a reference signal. We represent it as 50/30. basically, the signal is represented as Amplitude/Phase shift Note that the phase shifts are introduced due to inductors and capacitors present in the circuit.

Now suppose, this signal A is superimposed with a signal B of amplitude 10 and phase shift 15 degrees i.e. 10/15

The o/p of this superimposition cannot be found by direct mathematical addition of A and B. i.e. you cannot write 50/30 + 10/15 ≠ 60/45. This is mathematically wrong.

For this reason you find out the complex plane equivalent of the signals. Remember complex plane is composed of real numbers in horizontal axis and imaginary numbers on vertical axis. So an AC signal A is represented as follows:

Amplitude(A)= √(real(A)² + img(A)²)
Phase shift(A) = arctan(img part(A)/real part(A))

Hence signal (A) in complex plane= real(A)+j.img (A)

And there you have your complex number representing an electrical signal.

To cut short a long story, the imaginary number is basically used to account for the phase shift mathematically. Consider these two statements:

-You cannot physically see the imaginary part but you can see the effect of phase shift represented in complex plane as explained above.
- Vice versa, you can see the effect phase shift represented in complex plane as explained above, but you cannot see the presence of imaginary part physically.

Hope this helps.

 

[sanaullah2015]

Thank you very much.:d


If complex number consist of magnitude and Phase ..And it gives the information of Magnitude and Phase shift,

Referring a very nice example you mentioned..........Then why do we have to Square ,ADD and Square Root the real and Imaginory of Signal A to get the Magniuted and take arc Tan to get the phase shift??

DOes the Singal A represented in Complex Number With Real and Imaginory do not give the Information of Magniuted and phase shift of the same signal??

??

Waiting for you reply.
Regards

 

[eltonjohn]

To understand complex number ..First at all don't call it COMPLEX .Is not complex but simple .In the UNIVERSE we live in there are quantities that have several dimensions .
Think about a bag of potatos and apples .Well such a bag has a weight .and a size .Such physical entities in the universe exist and to be able to express them we need some sort of bin or holder for each dimensional value .Vectors were invented to express such entities .The same way that vector dimensions operations yield other vectors dimensions .The complex number system is just another type of vectorial system where the vector I has different operation properties than the real number .The reason why we think that imaginary numbers are such a weird thing is that they were "invented" before the vectorial concept
Otherwise we will have complex numbers expressed in vectorial notation
like this A = xr + yi where r and i are vectors such 1=r.r and -1 = i.i and of course
r.i = i.r = i ( i has the agebraic propetry to be abosorbant) .So basically r doesn't matters a lot in any computation .. well we can get rid off of it to save some extra space. And still is implied that dim(A) =2

 

[siongboon]

Hi,

I think the complex number as a numbering system
to describe a 2D numbering system.

A single dimension information is 1234567890 like number on a ruler for example.
How do you represent the information in 2D.?
I think this explain the use of a complex number.
Any 2 dimension information can apply complex number.

example of 2D information:
Signal having Amplitude and Phase at the same instant of time.

I can't think of another example.
This is what I think of complex number.

Best Regards,
Siong Boon

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