How to relate complex number with physical meaning?

[pbs681]

complex number

hi,
How to relate complex number with physical meaning. i.e: why resistor only has real number while capacitor has both real and imaginary? And why we call imaginary?
thanks

 

[adedia]

complex number

Often, we use complex numbers in physics to simplify calculations - for example, the voltages and currents in an electronic circuit have real values, but in a.c. problems, where they change sinusoidally with time, we can represent them as complex numbers and thus include the amplitude and phase of the variation in one number. It then turns out that we can do arithmetic with these numbers to work out what is going on in the circuit, which is much easier than having to solve lots of coupled differential equations to get the form of the functions. But in this case, the underlying theory still deals in real quantities, and the complex numbers are 'just' a mathematical convenience, albeit one we couldn't do without.

However, there is in principle no reason why physical theories can only use real numbers. Of course, they must successfully predict the real values of distances, times, temperatures and so on that we can measure in experiments, but the theories themselves can contain complex numbers. In quantum mechanics, the wave-function 'y(x)'is in general complex, but it is analysed in such a way that it can make predictions about real numbers that can be observed in experiments. For example, the 'probability density' is given by |y(x)|2, which is real.

also
According to the great Feynman:-
Any standard oscillation generates a standard solution,
x = C1exp{ikt} + C2exp{-ikt}

This is complex.
The complex number is actually an easy way to put more information.

and
In solving a physical problem, complex numbers are often used as a mathematical convenience. The physical answer is usually the real part of the final answer. For instance, if an answer for x is x=exp(-iwt), the physical result is cos wt.

 

[helios]

Re: complex number

If we desire that every integer has an inverse element, we have to invent rational numbers and many things become much simpler.

If we desire every polynomial equation to have a root, we have to extend the real number field R to a larger field C of 'complex numbers', and many statements become more homogeneous.

A complex number
To construct a complex number, we associate with each real number a second real number.
A complex number is then an ordered pair of real numbers (a,b).
We write that new number as
a + bi

The '+' and the i are just symbols for now.

We call 'a' the real part and 'bi' the imaginary part of the complex number.


Ex :

(2 , 4.6) or 2 + 4.6i ;
(0 , 5) or 0 + 5i ;
(-5 , 36/7) or -5 + (36/7)i ;




similarly when it come to electricity / EMF we use complex number a lot cos it can have both i & ω component as i+ω




- helios

 

[pbs681]

Re: complex number

Thanks a lot for both of u. Now it become clear. But I still have 1 question. Why do we call imaginary part?

 

[flatulent]

Re: complex number

Thanks a lot for both of u. Now it become clear. But I still have 1 question. Why do we call imaginary part?

This goes back hundreds of years to mathematicians who were investigating the square root of negative numbers.

 

[jallem]

Re: complex number

in reality the complex number in circuit represent
a phase or time difference. If you think in terms
of Fourier transform cosine is just sine with a phase
difference(or viceversa). So a signal wihich a delayed
can be represented with a imaginary number

 

[amir1981]

complex number

complex number is not more than a vector

 

[ran_out]

Re: complex number

i recommed warmly chapter 8 "quadrature signals" in the book:

"understanding dsp" by lycons

its the best chapter i have read about this subject by far than other material

regarding this subject


the book is available on this forum

 

[sxianz]

Re: complex number

Excuse me ,I am a newer in this forum .

Can you tell me , How to get the Ebook in this forum .

Thank you !!

 

[phongphanp]

Re: complex number

Hi sxi... Sourry ! can't remember your full name. you must make your points
by Post or make Problem clear, more and more answers will make your point up.

 

[anand_hdl]

Re: complex number

Fundamentally the idea behind complex number is as follows:
Curiously, the complex number model can be used in a significant way as an aid in solving difficult problems by representing and computing two variables as one. The technique is to let the non-interacting real and imaginary components of the complex number be holding places for different problem variables and perform a single simultaneous complex computation for them.

Better way of solving some type of problems.

Refer to the Link below on more details:
**broken link removed**