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Re: Separating real part and imaginary part from each
*To*: mathgroup at smc.vnet.net
*Subject*: [mg101247] Re: [mg101189] Separating real part and imaginary part from each
*From*: Bob Hanlon <hanlonr at cox.net>
*Date*: Sat, 27 Jun 2009 06:07:44 -0400 (EDT)
*Reply-to*: hanlonr at cox.net
f[z_] = (a*z + b)/(c*z + d);
g = f[x + I*y];
g // ComplexExpand // FullSimplify
(a*x + I*a*y + b)/(c*x + I*c*y + d)
FullSimplify[ComplexExpand[#]] & /@ (Re[g] + I*Im[g])
((a*x + b)*(c*x + d) + a*c*y^2)/
(c^2*y^2 + (c*x + d)^2) +
(I*(a*d*y - b*c*y))/(c^2*y^2 +
(c*x + d)^2)
% == %% // Simplify
True
Bob Hanlon
---- Alexander <alexander.erlich at gmail.com> 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
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