Azrael84 wrote:

Nice solution. I believe there are few typos, equation (1) should really look like:

z=z_0+re^{it}, but this doesn't affect the proof obviously. Also on the last page I think you mean to take z_0=x_0+iy_0 (missing an i as z_0 is complex constant), again just some typos hopefully make it easier for those going through your proof.

Thanks for reading my solution. I'm glad you like it!

I agree that on the last page it should be

z_0=x_0+iy_0, but I don't agree with your first point.

r is a complex number here and so

z=z_0+r is correct. That's why I called it a radius

vector in line 1. I think that I should have added

|r|=constant to make it clearer.

As

z changes so does

r, but only the argument of

r changes not its modulus.

I will amend my first post above and upload a corrected and amended pdf file.