Complex numbers - loci

[IceMan]

struggling with loci
What is the locus of
1) |z-3-2i|=|z+5-6i|
2) |6z-1|=13
where z is a complex number

[KatieB]

1) |z-3-2i|=|z+5-6i|

Any thing of the form |z-a|=|z-b| represents the perpendicular bisector of a and b


|z-3-2i|=|z+5-6i| should be written in this form as |z-(3+2i)|=|z-(-5+6i)|
so this is the perpendicular bisector of (3+2i) and (-5+6i)

2)
|6z-1|=13

Again anything of the form |z-a|=r represents a circle radius r and centre a

|6z-1|=13
|6(z-1/6)|=13
6|z-1/6|=13
|z-1/6|=13/6

Circle centre (-1/6,0) radius 13/6