Date: May 27, 2013 4:20 AM
Author: emammendes@gmail.com
Subject: Re: How to use Mathematica find the solution of an
Many thanks for the reply.

If we consider

1/((I w)(1+I w)^2)

we have

-angle(I w)-2*angle(1+I w) = -180

-90-2*angle(1+ I w)=-180

-2*angle(1+i w)=-90

angle(1+iw)=45

therefore w = 1

and probably something similar for w=-1.

I feel that I do not know how Mathematica deals with the argument of a complex number.

To be honest I would like to know what is going on under the hood of PhaseMargins.

Many thanks

Ed

On May 24, 2013, at 7:23 AM, Bob Hanlon <hanlonr357@gmail.com> wrote:

>

> The equation does not appear to have a solution except as a limit (from

> below) but then the solution is either -1 or 1.

>

>

> eqn = Arg[-(I/((1 + I w)^2 w))] == -Pi;

>

>

> eqn // Simplify

>

>

> False

>

>

> eqn /. {{w -> -1}, {w -> 1}}

>

>

> {False, False}

>

>

> Limit[Arg[-(I/((1 + I w)^2 w))],

> w -> -1, Direction -> 1] == -Pi

>

>

> True

>

>

> Limit[Arg[-(I/((1 + I w)^2 w))],

> w -> 1, Direction -> 1] == -Pi

>

>

> True

>

>

>

> Bob Hanlon

>

>

>

>

> On Thu, May 23, 2013 at 4:04 AM, Eduardo M. A. M. Mendes <

> emammendes@gmail.com> wrote:

>

>> Hello

>>

>> I need to solve the following equation:

>>

>> Arg[-(I/((1+I \[Omega])^2 \[Omega]))]==-\[Pi]

>>

>> I have tried Solve (empty output), Reduce (it gives some results but not

>> the answer Omega=1) and FindRoot (it gives Omega=1 but it is a

>> numerical search). Is there a way to get the solution not using a

>> numerical search?

>>

>> Many thanks

>>

>> Ed

>>

>> PS. I need to solve several equation of the same kind.

>>

>>