Is there a way of directly sketching a graph like |z - 1| = |z - 2i| on CAS without converting to Cartesian form by hand?

You should be able to recognise that graph

or you will be able to with time.

The graph |z - 1| = |z - 2i|

means the distance of some point from 1 is the same distance from the point 2i on the complex plane.

Therefore the graph required is the line that is the perpendicular bisector of the points 1 and 2i.

Now let's consider the cartesian plane where the points are (1,0) and (0,2)

the mid point is M (1/2,1)

The gradient between the points is rise/run = -2/1 = -2

We need the perpendicular bisector

y-y = m(x-x)

It is perpedicular so m = -1/-2 = 1/2

and passes through (1/2,1)

so

y - 1 = 1/2 (x -1/2)

y = 1/2x -1/4 + 1

y = 1/2x +3/4

Note you normally wouldn't actually need to find the equation of the line just graph it. make sure you do so indicating that the line is perpendicular and the same distance away as the image suggests. In this case A is 1 and B is 2i

hope this helps