# using function Abs on complex number

**URL:** <https://community.wolfram.com/t/using-function-abs-on-complex-number/4595>\
**Category:** Questions\
**Tags:** mathematica, algebra\
**Created:** [January 23, 2015, 2:14pm UTC](https://community.wolfram.com/t/using-function-abs-on-complex-number/4595 "2015-01-23T14:14:30Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![jga2008](https://avatars.discourse-cdn.com/v4/letter/j/4491bb/32.png) [@jga2008](https://community.wolfram.com/u/jga2008)\
**Post date:** [January 23, 2015, 2:14pm UTC](https://community.wolfram.com/t/using-function-abs-on-complex-number/4595/1 "2015-01-23T14:14:30Z")

</div>

I am having some difficulty when dealing with complex number using mathematica function Abs.  
I am trying to use Abs[1+ I w] to get Abs[1+ I w]=Sqrt[1+ w^2]. But, it seems that I can’t do it in a straight forward way. That is

```
  $Assumptions = \[Omega] \[Element] Reals
    Abs[1 + I \[Omega]]

```

Using the above lines, I don’t get the right answer. After reading some previous post related with complex numbers, I tried to use ComplexExpand function.

```
 ComplexExpand[Abs[1 + I \[Omega]], TargetFunctions -> {Re, Im}]

```

Using the above function, I get the right answer.

My question is why I failed in the first attempt, or what is the logic that Abs[1 + I [Omega]] will not give me what I want. Is there a way to get the expected answer by using Abs.

Many thanks

---

<div class="post-metadata">

**Author:** ![franciscoj](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/franciscoj/32/35674_2.png) [@franciscoj](https://community.wolfram.com/u/franciscoj)\
**Post date:** [January 23, 2015, 4:29pm UTC](https://community.wolfram.com/t/using-function-abs-on-complex-number/4595/2 "2015-01-23T16:29:31Z")

</div>

If you see documentation:

> `Abs[z]` is left unevaluated if z is not a numeric quantity.

So it has always to be forced with `ComplexExpand`, which also works without any option by the way.