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samnatha

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

  • one year ago
  • one year ago

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  1. phi
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    I think they want you to write 8 as \[ 8=8(\cos(2 \pi) + i \sin(2 \pi))\]

    • one year ago
  2. samnatha
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    well the theorm we have been using is diff cuz u have to add 2n(pi)

    • one year ago
  3. phi
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    yes, that is even better. 8=8(cos(2nπ)+isin(2nπ))

    • one year ago
  4. samnatha
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    like the way our teacher has been telling us is we have to get this \[\sqrt[3]{8?}\]

    • one year ago
  5. samnatha
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    then it is 2 to the power of a third

    • one year ago
  6. phi
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    See http://en.wikipedia.org/wiki/De_Moivre's_formula#Applications you solve \[ \left( z^3 \right)^{\frac{1}{3}} = 8^{\frac{1}{3}}(\cos(2n\pi)+i \sin(2n\pi)^{\frac{1}{3}}\]

    • one year ago
  7. phi
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    you get 3 different answers, for n=0,1,2. then they start repeating n=3 gives the same answer as n=0

    • one year ago
  8. samnatha
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    yeah i kinda get thanks

    • one year ago
  9. samnatha
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    wait usually ther is another angle you can't get 0 of 2n pi

    • one year ago
  10. phi
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    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))

    • one year ago
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