Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

samnatha

  • one year ago

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

  • This Question is Closed
  1. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  2. samnatha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    well the theorm we have been using is diff cuz u have to add 2n(pi)

  3. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes, that is even better. 8=8(cos(2nπ)+isin(2nπ))

  4. samnatha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    like the way our teacher has been telling us is we have to get this \[\sqrt[3]{8?}\]

  5. samnatha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then it is 2 to the power of a third

  6. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  7. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you get 3 different answers, for n=0,1,2. then they start repeating n=3 gives the same answer as n=0

  8. samnatha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah i kinda get thanks

  9. samnatha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wait usually ther is another angle you can't get 0 of 2n pi

  10. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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))

  11. Not the answer you are looking for?
    Search for more explanations.

    Search OpenStudy
    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.