solve 2 unknowns using one complex equation

usually, to solve 2 unknowns, it require at least 2 or more equations. but if the equation is complex, then one equation is sufficient since can compare the real and imaginary part. for example

3+2i = (x+2y+1)+(2x-y-3)i

if want to solve for x and y a simple solve function as shown can be written.

T=3+2i;
syms x y;
P=-real(T)+ (x+2*y+1);
Q=-imag(T)+ (2*x-y-3);
R=solve(P,Q);
X=R.x
Y=R.y

I am now trying to tackle a much more complex equation that involves x and y. and its near impossible to separate the terms into real and imaginary part.

so i'm hoping to do something like this

    syms x y;
    P=-1*real(T)+ real(%a complicated eq relating x&y%);
    Q=-1*imag(T)+ imag(%a complicated eq relating x&y%);
    R=solve(P,Q);

but i keep getting error. i think the syntax is incorrect. is there a way to get this working? please share your thoughts one this.

any suggestions are highly appreciated.

[Walter Roberson]

What error message do you get?