Re: Finding real part (newbie question)

• To: mathgroup at smc.vnet.net
• Subject: [mg15787] Re: Finding real part (newbie question)
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Sun, 7 Feb 1999 02:04:04 -0500 (EST)
• References: <79e8lo\$9du@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Gnalle wrote in message <79e8lo\$9du at smc.vnet.net>...
>If a,b,c,d are real numbers. How do I use mathematica to find the real
>part of
>
>1/(a + I b + 1/(c + I d))
>
>Yes I can calculate it by hand, but I would like to know how to use
>Mathematica.
>--
>
> Niels Langager Ellegaard
> 'http://mmf.ruc.dk/~gnalle/'
>
Niels:

In[1]:=
ComplexExpand[Re[1/(a + I b + 1/(c + I d))],
TargetFunctions->{Re,Im}]

Out[1]=
a/((a + c/(c^2 + d^2))^2 + (b - d/(c^2 + d^2))^2) +
c/((c^2 + d^2)*((a + c/(c^2 + d^2))^2 +
(b - d/(c^2 + d^2))^2))

If you will need to do this a lot in the session you can set the option
TargetFunctions once and for all with

In[2]:=
SetOptions[ComplexExpand , TargetFunctions->{Re,Im}];

Then

In[3]:=
ComplexExpand[Re[1/(a + I b + 1/(c + I d))]]

Out[3]=
a/((a + c/(c^2 + d^2))^2 + (b - d/(c^2 + d^2))^2) +
c/((c^2 + d^2)*((a + c/(c^2 + d^2))^2 +
(b - d/(c^2 + d^2))^2))

In[4]:=
ComplexExpand[Re[Log[Sin[x+I y]]]]

Out[4]=
1/2*Log[Cosh[y]^2*Sin[x]^2 + Cos[x]^2*Sinh[y]^2]

Allan

---------------------
Allan Hayes
Mathematica Training and Consulting
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

```

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