anonymous
  • anonymous
please help me i have some idea of what to do but i need help ! use de moivre's theorem to solve each of these questions. plot your solutions on the complex plain. (i) z^3 = 8
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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phi
  • phi
I think they want you to write 8 as \[ 8=8(\cos(2 \pi) + i \sin(2 \pi))\]
anonymous
  • anonymous
well the theorm we have been using is diff cuz u have to add 2n(pi)
phi
  • phi
yes, that is even better. 8=8(cos(2nπ)+isin(2nπ))

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anonymous
  • anonymous
like the way our teacher has been telling us is we have to get this \[\sqrt[3]{8?}\]
anonymous
  • anonymous
then it is 2 to the power of a third
phi
  • phi
See http://en.wikipedia.org/wiki/De_Moivre's_formula#Applications you solve \[ \left( z^3 \right)^{\frac{1}{3}} = 8^{\frac{1}{3}}(\cos(2n\pi)+i \sin(2n\pi)^{\frac{1}{3}}\]
phi
  • phi
you get 3 different answers, for n=0,1,2. then they start repeating n=3 gives the same answer as n=0
anonymous
  • anonymous
yeah i kinda get thanks
anonymous
  • anonymous
wait usually ther is another angle you can't get 0 of 2n pi
phi
  • phi
in case it is not clear 8 = 8( cos(0) + i sin(0)) when we add in multiples of 2π we get 8 = 8( cos(2nπ ) + i sin(2nπ))

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