EDIT: Its done

Hi there, I have to prove this two sentences . I think I've solved the first, but I'm quiet stuck with the second.

The first says:

1) Demonstrate that the equation of a line or a circumference in the complex plane can be written this way: , with

So I called z and beta:

Then developing the products I get:

And making alpha equal zero I get the equation for a line, right? (for u and v fixed).

Then completing the square and reordering:

This is the equation for the circle, is this right?

In the other hand I got:

2) Prove that the geometrical place for the points that verifies is a circumference ( ).

I couldn't make much for this. I called z=x+iy again:

I don't know what to do from there.

Bye.

(Sorry if this topic doesn't belong here, please move it, I didn't know where to post so I posted here, and sorry too if it bothers you that I made two questions in the same topic, but I thought it was quiet trivial and it didn't deserved two different topics, but I can split it if necessary).