Re: How to use Mathematica find the solution of an

```By direct substitution:

1/((I w) (1 + I w)^2) /. w -> 1
-1/2

Arg[%]
Pi

The argument is NOT -Pi ! We're dealing here with the principal argument Arg, as usual. If you want to use some other branch of the multivalued function arg, that's your right, of course.

The expression has exactly the same value, -1/2, for w -> -1, so the same issue arises.

On May 27, 2013, at 4:24 AM, "Eduardo M. A. M. Mendes" <emammendes at gmail.com> wrote:

> 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 at 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 at 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.
>>>
>>>
>

---
Murray Eisenberg                                    murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower            phone 413 549-1020 (H)
University of Massachusetts                               413 545-2838 (W)
710 North Pleasant Street                         fax   413 545-1801
Amherst, MA 01003-9305

```

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