Loci on the Argand Plane

Finding loci is a demanding task that requires a robust background in geometry. Even skilful students struggle with it. In one of our last year's FP2 lessons, we were discussing loci on the Argand plane and we found out how challenging it is to understand and construct the loci of the complex numbers z that comply with this :
mod(z-z1)/mod(z-z2)=constant 
or 
arg(z-z1)-arg(z-z2)=constant 
where z1 and z2 are known complex numbers. 

As we all know, you cannot understand a locus until you have constructed it by yourself. Moreover, demonstrations -no matter how meticulously they could have been made by the teachers- fail to really persuade students that what they see is actually what they are looking for. 
We also know that GeoGebra can be used to facilitate understanding in a brilliant way. 

The modulus -argument form of a complex number (the polar form as it is better called) gives us a tremendously convenient way to explain and visualize our loci. We can ask students to use Geogebra to construct complex numbers with the properties that a particular locus requires, place them on the Argand plane and turning the  'trace' on to move them so that they can find out how the loci looks like. We can also ask them to use the Locus inherent command in Geogebra to verify their findings. 
They can get their toe into water and experiment changing the variables’ values  or the  positions of the numbers the construction is based on. Geogebra at this level is as easy to be used by them as any graphic calculator, but far more suitable for this learning goal. Furthermore, it’s worth getting familiarized to this environment as well (so they will not be ‘afraid’ of subjects like ‘fm with technology’) 

Below you can find a link towards a ‘book’ containing  Geogebra files which correspond  to the basic loci problems we meet in FM1 and FM2 under the ‘Complex numbers’ topic.  All of them can easily be made by the students themselves under a really little help. 
https://ggbm.at/n75NZYwC