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Monic polynomial of the lowest possible degree

  1. May 30, 2016 #1
    1. The problem statement, all variables and given/known data

    A monic polynomial is a polynomial which has leading coefficient 1. Find the real, monic polynomial of the lowest possible degree which has zeros −1−2i,−2i and i. Use z as your variable.


    3. The attempt at a solution

    Would I just expand the zeros giving me

    (z+1+2i)(z+2i)(z-i)

    z^3+(1+3*I)*z^2+I*x+I*4+2
     
  2. jcsd
  3. May 30, 2016 #2

    SammyS

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    Don't forget: It's a real polynomial.
     
  4. May 30, 2016 #3
    how would I make it real?
     
  5. May 30, 2016 #4

    SteamKing

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    Hint: what happened to the conjugates of the original roots?
     
  6. May 31, 2016 #5
    Does that mean that I have to square the imaginary roots?
     
  7. May 31, 2016 #6

    SteamKing

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    What is the conjugate of the complex number, a + bi?
     
  8. May 31, 2016 #7

    SammyS

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    @53Mark53 ,
    Here's what you said in a previous thread:
    The same applies here, but now you have 3 complex roots, no two of which form a conjugate pair.
     
  9. May 31, 2016 #8
    Thanks I got the right answer by using conjugate pairs
     
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