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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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