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 z3-1=0
- Use graphing software to plot these roots on an Argand diagram as well as a unit circle with centre origin.
- Choose a root and draw line segments from this root to the other two roots.
- Repeat those above for z4-1=0 and z5-1=0, comment your result and try to formulate a conjecture.
- Prove your conjecture.
- Use de Moivre's theorem to obtain solutions to Zn=i
- Represent each of these solutions on an Arganda diagram
- Generalize and prove your result for Zn=a+bi, where /a+bi/ = 1
- What happens when /a+bi/ is not equal to 1