Importance of Geometry for Complex Numbers (1 Viewer)

[Drongoski]

Over the last 40 years or so, geometry has not received as much attention as they used to. Many questions on complex numbers are better approached by geometry (easier, shorter, visually-clearer, neater solutions). So if you want to do well in complex numbers, make sure you have a good foundation in elementary high school geometry: properties of parallel lines, parallelograms, rhombuses, squares, isosceles triangles, congruent triangles, similar triangles, circle geometry(learn this yourself if necessary), etc, etc.

Geometry is where we first learn about logical deduction: how to prove a proposition, each step with supporting reasons. Elementary geometry is deceptively simple; but I suspect more than half of the students in Yr 6, 7 . . . 10 often miss the deeper and/or subtler implications.

I notice many students have difficulty with proofs in complex numbers, because they are not strong in their geometry.

 

[CM_Tutor]

I very much agree, and the stripping of geometry from Advanced, MX1, and MX2 is problematic for this reason. It is highlighted by problems with vector proofs in MX1 and in various parts of MX2 including complex numbers. I have recently posted an algebraic solution to what should be handled geometrically to highlight the problem, and particularly to illustrate that the algebraic approaches can make the restrictions on the domain difficult to recognise.