Re: Finding real part (newbie question)

• To: mathgroup at smc.vnet.net
• Subject: [mg15762] Re: Finding real part (newbie question)
• From: Stephen P Luttrell <luttrell at signal.dra.hmg.gb>
• Date: Sun, 7 Feb 1999 02:03:45 -0500 (EST)
• Organization: Defence Evaluation and Research Agency
• References: <79e8lo\$9du@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```>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.

This should do what you want:

In[1]:=ComplexExpand[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) -
(I*b)/((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)) +
(I*d)/((c^2 + d^2)*((a + c/(c^2 + d^2))^2 +
(b - d/(c^2 + d^2))^2))

Stephen P Luttrell
Signal Processing and Imagery Department DERA Malvern, St.Andrew's Road
Malvern, United Kingdom, WR14 3PS

+44 (0)1684 894046 (tel)
+44 (0)1684 894384 (fax)
luttrell at signal.dera.gov.uk (email)

```

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