Complex Loci

SparksMaths shared this idea 1 year ago
Under Consideration

I recently was shown that loci described in terms of complex numbers can be plotted easily as follows:

Half Line from (3,2) at pi/4 to horizontal:

arg((x,y)-(3+2i))=pi/4


Circle centre (-1,3) radius 3

abs((x,y) - (-1+3i))=3

This is great, but I have two questions:

  1. It would be more useful from a teaching point of view to be able to write the 'general point' ((x,y) in the examples), which is often written as 'z' in textbooks, as x+iy. When I try this with the argument function - the half line - (e.g. arg(x+iy-(3+2i))=pi/4 ) - it seems to work fine. Hooray! When I try it with the absolute function - the circle - it does not (e.g. abs(x + ί y - (-1 + 3ί)) = 3. Can this be fixed, or am I missing something? Screenshot attached
  2. Can we get these implicit curves to define regions of the plane by using inequalities rather than equations in these constructions? (e.g. abs(x + ί y - (-1 + 3ί)) < 3)?

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