Thread: Patterns from complex numbers (Part A & B)

1. Patterns from complex numbers (Part A & B)

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.

Part B
• 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

2. Re: Patterns from complex numbers (Part A & B)

This is quite a large assignment you are expecting help with. What have you done so far?

3. Re: Patterns from complex numbers (Part A & B)

$\displaystyle z^3 =1$

$\displaystyle Let z = rcis(\theta)$

$\displaystyle r^3cis(3\theta) = cis(0)$

Equate the angles and the r values

4. Re: Patterns from complex numbers (Part A & B)

Hi, it would be enough if you help me with the first two points of part A and the first point of part B.
Thank you.