# Math Help - Complex Transformation

1. ## Complex Transformation

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

Here's the question:

The transformation $T$ from the complex z plane to the complex w plane is given by $w = \frac{z+1}{z+i}$.

Show that $T$ maps points on the half line $arg{z} = \frac{\pi}{4}$ into points on the circle $|w| = 1$ in the w plane.

The way I did this is by $|\frac{z+1}{z+i}| = 1$, leading to $|z+1| = |z+i|$.

Now if we map the loci of these points we get the half line $arg{z} = \frac{\pi}{4}$.

Just a few questions, firstly is this right? Is it ok to do it this way, instead of starting with the $arg{z} = \frac{\pi}{4}$, and is there another way to do this?

Thanks in advance for the help

2. Anyone any ideas?