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Math Help - Patterns from complex numbers (Part A & B)

  1. #1
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    Exclamation 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
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  2. #2
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    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?
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  3. #3
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    Re: Patterns from complex numbers (Part A & B)

     z^3 =1

     Let z = rcis(\theta)

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

    Equate the angles and the r values
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  4. #4
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    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.
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  5. #5
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    Re: Patterns from complex numbers (Part A & B)

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