Hi again, just a quick question about a transformation in the complex plane.

Here's the question:

The transformation from the complex z plane to the complex w plane is given by .

Show that maps points on the half line into points on the circle in the w plane.

The way I did this is by , leading to .

Now if we map the loci of these points we get the half line .

Just a few questions, firstly is this right? Is it ok to do it this way, instead of starting with the , and is there another way to do this?

Thanks in advance for the help