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Complex numbers basics

  1. May 13, 2016 #1
    1. Give a formula for the values on m such that z^m=z

    z=cos(7pi/6)+i*sin(7pi/6)

    2. If i use de movires i get

    3. m*7pi/6=7pi/6 + k*2pi

    But then i get the value that k=12/7, Which is the wrong formula.

    The correct answer is 1+12k for k=0,1,2...
     
  2. jcsd
  3. May 13, 2016 #2

    SammyS

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    What happened to m in your answer?

    Can you show us your work ?
     
  4. May 13, 2016 #3
    m*7pi=7pi+k*12pi
    m=1+12k/7

    Okay, i got closer to the right answer now

    Which is the equation wolfram alpha also get if i post my original equation. So it must be something wrong!!!

    1+12k is the correct!!
     
  5. May 13, 2016 #4

    SammyS

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    You have ##\ m=1+\frac{12}{7}k\,,\ ## & k must be some integer. I suppose from the context of the question that m must also be an integer.

    m will only be an integer if k is an integer multiple of 7 , Right ?

    let k = 7n .
     
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