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.
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.