So the solutions to the n'th roots of unity of the form z^n = 1 are n-gons on the unit circle. This means for an arbitrary w in the complex field z^n = w gives solutions on a circle with radius n'th root of modulus w and are 2*pi/n apart so it is also an n-gon.
Pretty fun stuff to plot around using Geogebra to give a geometric intuition how the complex numbers behave.
I’m curious as to how many high schools around the world teach complex numbers. In England in the late 80s when I did A level maths (age 17-18) it was part of the syllabus, but now it is only available in the harder A-level further maths, which is often not taught in the standard non-selective non-private schools, making entry to university STEM courses more difficult.
In Portugal it is part of the standard curriculum although in my time they were poorly motivativated and besides solving some classes of quadratic equations no other applications were mentioned.
So the solutions to the n'th roots of unity of the form z^n = 1 are n-gons on the unit circle. This means for an arbitrary w in the complex field z^n = w gives solutions on a circle with radius n'th root of modulus w and are 2*pi/n apart so it is also an n-gon.
Pretty fun stuff to plot around using Geogebra to give a geometric intuition how the complex numbers behave.
Reading this made me feel like I am in highschool again
I’m curious as to how many high schools around the world teach complex numbers. In England in the late 80s when I did A level maths (age 17-18) it was part of the syllabus, but now it is only available in the harder A-level further maths, which is often not taught in the standard non-selective non-private schools, making entry to university STEM courses more difficult.
In Portugal it is part of the standard curriculum although in my time they were poorly motivativated and besides solving some classes of quadratic equations no other applications were mentioned.