Help with Complex Polynomial equation in mathematica

[Don Diego]

Hi everybody:
I'm trying to analyse equations of analogue electronic filters, but i can't get the "norm" of the complex polynom if i use variables (or symbols? what's the difference?), here's the simplest exemple (RC low pass filter, a represents R*C*w, reals variables > 0):

Assuming[ a \[Element] Reals && a > 0, Norm[1/(1 + a \[ImaginaryJ])]]

Norm[1/(1 + I a)]

The answer :

Norm[1/(1 + I a)] ----- the same thing!

Re[] and Im[] doesn't work either!
I will like to uses to find the argument (Arg[] doesn't work)

and after all, make my bode plots!
please help me, I'm new in mathematica!
Thanks

 

[Don Diego]

up?? somebody?? help!

 

[Hurkyl]

Norm? Do you mean Abs?

If you want it to try and simplify things, or expand a function, or other stuff, you should invoke the appropriate functions...

And if you want to plot something, just plot it. If it evaluates to a real number, it doesn't matter what the symbolic form is.

 

[Don Diego]

Hi Hurkyl, and thanks for the answer:

My problem is that i can't get the "modulus" or "norm" of the Complex number, once i get the norm (norm = abs) i would like to plot it as a fonction of "w", how can i get the Norm of à complex number without fixed values??
exemple:
Norm[1/(1 + 3 \[ImaginaryJ])]
then i get :
1/Sqrt[10]

with Norm[(1/(1 + a \[ImaginaryJ]))
i get Norm[(1/(1 + a \[ImaginaryJ])), the same thing!

i should get : 1/(\[Sqrt]1 + a^2)
... what ca i do?

 

[Hurkyl]

What part of my response didn't you understand?

 

[guerom00]

Yeah, it's a drag…
For your particular example, this gives the appropriate result :

http://img185.imageshack.us/img185/319/picture1qs.jpg

I suggest you define a function which does the above

 

[Don Diego]

GREAT GREAT! I'm going to try this! Thanks so much gueromm00! you are great!
I'm going to put my results with à more complex filter!
:):):)! thanks!

 

[Don Diego]

Voila Voila!
RLC Low pass filter in the attachement!
thanks a lot!

 

[Hurkyl]

Why are you bothering trying to coerce Mathematica to express it in a particular symbolic form when all you really want to do is plot it?

 

[guerom00]

Why are you bothering trying to coerce Mathematica to express it in a particular symbolic form when all you really want to do is plot it?

Well, in my case at least, when simply using the Abs[] function Mathematica hangs when trying to plot…
So, it does make sense to help him a little
I think it is because of the Manipulate[]… (otherwise, I agree with you : since all plots functions have an HoldAll attribute, it doesn't matter what symbolic form its argument evaluates to)

 

[Don Diego]

This was just un exemple, what i really want to do it's to manipulate the complex expressions in a theorycal way, I'm learning about filters ok?, i don't want to just plot something without understanding the original relation. my problem was just about the manipulation of complex equations and now it's OK.
Thanks guerom00, you're really nice!

 

[Hurkyl]

That's fair. It's hard for me to tell, since you didn't really respond to any of my earlier comments.

I am mildly surprised that you cannot just FullSimplify your original expression (with an assuming clause), or possibly ComplexExpand it. Or... was that just not tried? Ah well, I forgot to play with it earlier when I had a chance.

 

[Don Diego]

Sorry Hurkyl, but I'm new in mathematica, i didn't know about "complexexpand"... i think that you didn't realize that I'm a newbie, i don't understant everything about mathematica, thanks for yours comments ;)

 

[Don Diego]

Hi!
Now i have one new problem, i can't run this Laplace equation (see attachement)

I don't know what to do, sorry... please help me!
Thanks!

See the "InverseLaplaceTransform" don't show me the answer... why?

 

[Hurkyl]

When I made my reply, I was keying in on your desire to plot, which doesn't require manipulating things into a "nice" form. I was hoping that if you were less interested in plotting and more interested in "simplifying things" or "expand a function"... or that it would prompt you to look up the keywords "simplify" or "expand" in the help.

Have you looked through Mathematica's documentation center? (e.g. under the "help" menu, or by hitting F1 after highlighting a word) It's pretty good. I didn't know about ComplexExpand myself, but I expect it's not hard to find if you started with the page for Expand or Simplify. I think there's even an article on "simplifying functions" but it's been a while since I looked at it.