Hi, I got my new internal assessment in math today and I found it quite complicated at some points. So, I'd appreciate if you could help me out.

It goes like this:

- Use de Moivre's theorem to obtain solutions to the equation z
^{3}-1=0- Use graphing software to plot these roots on an Argand diagram as well as a
unit circlewith centre origin.- Choose a root and draw line segments from this root to the other two roots.
- Repeat those above for z
^{4}-1=0 and z^{5}-1=0, comment your result and try to formulate a conjecture.- Prove your conjecture.

Part B

- Use de Moivre's theorem to obtain solutions to Z
^{n}=i- Represent each of these solutions on an Arganda diagram
- Generalize and prove your result for Z
^{n}=a+bi, where /a+bi/ = 1

- What happens when /a+bi/ is not equal to 1

P.s. I posted the same thread in algebra forum too because I thought this question concerns both algebra and trigonometry.