Hi,

I know this locus is a circle, but only because I recognise the form, I cannot see how to show it algebraically.

$\displaystyle \arg(z-2)-\arg(z-2i)=\frac{3\pi}{4}$

I would like to find the centre and radius (or its equation).

The second part of the question asks to show that $\displaystyle \frac{|z-4|}{|z-1|}$ is constant on this circle, but I don't even know what it's asking for that one!

Any nudges in the correct direction would be great, not asking for a full solution, just some help getting started.

Cheers