Complex Numbers : Further Mathematics (A2-Level) : Mathematics Content Knowledge
Further Mathematics (A2-Level)
Question 1 of 9
1. How confident are you that
a. you can represent simple sets of complex numbers as Loci in the Argand diagram?
What this might look like in the classroom
These loci divide into two groups, the first three are fairly straightforward and should help the students consolidate their previous knowledge of loci, and equations of circles, and definitions of angles and so on.
The final example is much harder. Students would benefit from a slow run through the explanation, perhaps with some pre-printed instructions with some parts missing – so that they can fill in the gaps, or explain what has been done to move from one line to the next.
Students should also be able to work backwards - when presented with a some sketches of loci they ought to be able to write the equation that would produce that sketch, or perhaps match up equations to loci. The more time spent helping students become familiar with the four loci the easier they will find remembering the four types later in the course.
Taking this mathematics further
Students would do well to consider additional loci – in order to stretch their minds further. Can they picture what would be necessary in order to draw a spiral? Or perhaps they can start to think in three dimensions – a sphere? A plane?
The equation of a circle has been seen before, and students should find little difficulty in linking the circle drawn on the complex plane with their previous knowledge of coordinate geometry. The perpendicular bisector has similar links to coordinate geometry.
The half-line is a newer concept but the students might be drawn into a useful discussion about infinity. Examples of helpful aspects of infinity can be found in the external links section below.
Related information and resources from other sites