Symbolic complex number manipulation

Is there a way to put a fraction of complex number in standard form with the symbolics toolbox? After getting it in standard form simplify to then extract the imaginary part? And lastly, setting the imaginary part equal to zero and solving for a variable?

for example:

Z=(A+1i*B)/(C+1i*D)
%%should give the following in closer to standard form, not done automatically
Z2=(A+B*1j)*(C-D*1j)/(C^2+D^2)
%%trying to simplify
Z3=collect(Z2,1i)
%%this command should give the imaginary part, but just marks in the equation imaginary and real. 
Z3imag=imag(Z3)

Answer 1

[Walter Roberson]

syms A B C D real

and then do your steps. This gives (B*C - A*D)/(C^2 + D^2) as the result.