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Please help with this complex number question

  1. Apr 22, 2012 #1
    find all solutions to z^2+4z ̅+4=0 where z is a complex number. Please help with this qn i'm having difficulty. thanks
     
  2. jcsd
  3. Apr 22, 2012 #2

    Office_Shredder

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    It's a quadratic polynomial. Do you not know how to factor these/the quadratic formula?
     
  4. Apr 22, 2012 #3
    so is the answer just 2i^2???
     
  5. Apr 22, 2012 #4
    or is it 2?
     
  6. Apr 23, 2012 #5
    That's a conjugate isn't it?

    Suppose so then you have:

    [tex]z^2+4\overline{z}+4=0[/tex]

    Then let [itex]z=a+bi[/itex]

    so:

    [tex](a+bi)^2+4(a-bi)+4=0[/tex]

    equate real and imaginaries to zero. That's two equations in two unknowns. Solve them.
     
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