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Homework Help: Complex constant from single root.

  1. Feb 3, 2012 #1
    1. The problem statement, all variables and given/known data
    Do not use a calculator for this problem. Express your answers using square roots and/or fractional multiples of x.

    Determine the complex constant c such that v is a root of: z6 - c = 0


    2. Relevant equations
    v = [itex]\sqrt{3} - j[/itex]


    3. The attempt at a solution

    I believe the following are true:
    1. There are 3 distinct roots for this equation.
    2. Each of the distinct roots will have a conjugate pair to ensure there is no middle term.
    3. If 2 is true, then two of the six roots are [itex]\sqrt{3} -j[/itex] and [itex]\sqrt{3} +j[/itex]

    z6 - c = 0 --> z6 = c. Yes, this is as far as I have gotten. I'm not sure how to figure out the other 4 roots.
     
  2. jcsd
  3. Feb 4, 2012 #2

    rude man

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    Homework Helper
    Gold Member

    c = z6
    v = √3 - j
    Use re = r(cosθ + jsinθ)
    Write v as exponential
    Solve for c
     
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