Consider the function $f:C^2\rightarrow C$ and it is defined by:
$f(z_a,z_b)=R(z_a)+iI(z_b)$
where $R(z_a)$ is the real part of $z_a$ and $I(z_b)$ is the imaginary part of $z_b$.
Can I write $f(z_a,f(z_b,z_c))=f(f(z_a,z_b),z_c)$ in this case?
I spotted where I went wrong.
My working:
$f(z_a,f(z_b,z_c))=R(z_a)+iI(z_c)=f(f(z_a,z_b),z_c)$
I have accidentally put down $f(z_a,f(z_b,z_c))=R(z_a)+iI(z_b)$ but still got $f(f(z_a,z_b),z_c)=R(z_a)+iI(z_c)$ in my previous working so my LHS is not same as RHS and could not find out the mistake by reading thought my handwriting. But once I typed it up, I spotted it.
So this equation is correct.