Why does Arg[z] remains unsolved while extracting Real & Imaginary Parts?

With regards to solving equations involving COMPLEX potentials,

After solving the differential equation of these potentials, and then after substituting the value of z = re^itheta (Polar form), and subsequently extracting the REAL and IMAGINARY parts from the solution, I still continue to have the unsolved Arg[z] term in it.

and the extracted ‘Real’ and ‘Imaginary’ parts obtained also seem incorrect!
Appreciate it if I could see what my error is.
I have also attached my short code file, FYI.

Thanks

Try:

Thanks, Mariuz. Yes, it did fix it.
However, I thought that the ‘ComplexExpand’ command for the ‘displacement’ should have resulted in the form u1 + i.u2

4.PNG

whereby, the 'Real & Imaginary parts (u1 & u2) extracted from the complex equation for ‘displacement’, should have NOT included ‘imaginary i’.

I am still unable to understand why the real & imaginary parts continue to include ‘imaginary i’.
I am expecting them to have the following final form

Hoping to hear back…

Complex Potential.nb (11.5 KB)