Re: Separating real part and imaginary part from each

• To: mathgroup at smc.vnet.net
• Subject: [mg101216] Re: [mg101189] Separating real part and imaginary part from each
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sat, 27 Jun 2009 06:02:00 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200906261050.GAA18233@smc.vnet.net>

```ComplexExpand is your friend in such situations. (For reasons I don't
know, it seems unknown to too many users.)  And of course you must use
correct Mathematica syntax (but no reason for those explicit * signs):

f[z_] := (a z + b)/(c z + d)
ComplexExpand[ f[x + I y] ]

Alexander wrote:
> Hi,
>
> suppose I have the expression
>
> f(z) = (a*z+b) / (c*z+d) with z=x+I*y
>
> I did the calculation by hand and was able to separate real part fom
> imag. part to obtain something like this:
>
> g=f(x+I*y) = Re(g) + I * Im(g)
>
> But I don't know how to do this in Mathematica. I tried FullSimplify,
> Together, Apart, they didn't work. Can you help me?
>
> Alexander
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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