Locus on the Argand plane

nokia8650

arg ((z-6)/(z-2)) = pi/4

a) Sketch the locus which represents z

b) find the cartesian equation of this locus.

Could someone please help me with both of these parts. I have started by simplifying to arg(z-6) - arg(z-2) = pi/4, and have then drawn the two arguments on a diagram, and found an angle represented by arg(z-6) - arg(z-2). However, I was wondering if there was an algebraic method of solving the problem.

Thanks