Complex constant from single root.

  • Thread starter DmytriE
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  • #1
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Homework Statement


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


Homework Equations


v = [itex]\sqrt{3} - j[/itex]


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.
 

Answers and Replies

  • #2
rude man
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c = z6
v = √3 - j
Use re = r(cosθ + jsinθ)
Write v as exponential
Solve for c
 

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