Re: Separating real part and imaginary part from each other

*To*: mathgroup at smc.vnet.net*Subject*: [mg101231] Re: Separating real part and imaginary part from each other*From*: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>*Date*: Sat, 27 Jun 2009 06:04:46 -0400 (EDT)*References*: <h2295a$hoj$1@smc.vnet.net>

In[28]:= f[z_] = (a*z + b)/(c*z + d) Out[28]= (b + a z)/(d + c z) In[29]:= g = f[x + I*y] Out[29]= (b + a (x + I y))/(d + c (x + I y)) In[31]:= ComplexExpand[Re[g] + I*Im[g]] Out[31]= (b d)/((d + c x)^2 + c^2 y^2) + ( b c x)/((d + c x)^2 + c^2 y^2) + (a d x)/((d + c x)^2 + c^2 y^2) + ( a c x^2)/((d + c x)^2 + c^2 y^2) + ( a c y^2)/((d + c x)^2 + c^2 y^2) + I (-((b c y)/((d + c x)^2 + c^2 y^2)) + ( a d y)/((d + c x)^2 + c^2 y^2)) Then Together[] on the real and imaginary parts and you get: (b d + b c x + a d x + a c x^2 + a c y^2)/( d^2 + 2 c d x + c^2 x^2 + c^2 y^2) + I ((-b c y + a d y)/(d^2 + 2 c d x + c^2 x^2 + c^2 y^2)) Cheers -- Sjoerd On Jun 26, 12:50 pm, Alexander <alexander.erl... 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