       Re: Forcing Re[]'s to be Real

• To: mathgroup at smc.vnet.net
• Subject: [mg18246] Re: [mg18223] Forcing Re[]'s to be Real
• From: "David Park" <djmp at earthlink.net>
• Date: Thu, 24 Jun 1999 14:24:25 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Anthony Foglia wrote:

> I seem to have found an interesting problem involving computing the
>real part of complex numbers.  (Interesting, in that it wasn't there a few
>weeks ago when I ran the (as-far-as-i-can-remember) exact same code.)
>
>I have a complex function:
>
>k[w] := Sqrt[w^2 (1 + (2 / (1 + I w)))]
>
>I want to graph the real and imaginary parts, but Mathematica doesn't want
>to express the Re[k[w]] as a real number.  What do I mean?  Well, if I
>type:
>
>Re[Sqrt[1+I]]
>
>I get out
>
>Re[Sqrt[1+I]]
>
>Same if I do Re[ComplexExpand[Sqrt[1+I]]], or Re[(1+I)^(1/2)].  But if I
>enter:
>
>Re[ComplexExpand[(1+I)^(1/2)]
>
>Mathematica is kind enough to respond with:
>
>2^(1/4) Cos[Pi/8]
>
>I'm certain that this is the root of my problem, but I'll be damned if I
>know why Mathematica doesn't like it now, but did a few weeks ago.  Any
>help?
>
>--Anthony
>

Since, you want the real and imaginary parts for plotting purposes, you don't need
exact expressions and can use N on your expression.

Re[Sqrt[1 + I]] // N
1.09868

You probably used an approximate number in your expression several week ago.

David Park