complex numbers p6Watch
arg(z-1) - arg[(z-2i) = pi/4
By considering what this means geometrically and remembering circle theorems from year 11 or whenever you'll see it's the arc of a circle passing through A and B. Call P a point on the arc. Angle APB = pi/4.
Sub z=1+3i into arg[(z-1)/(z-2i)] and see if it's pi/4.