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Multiplying complex numbers

  1. Nov 23, 2012 #1
    Ok there is no way I am writing out all the work of this question using a keyboard, and my scanner chose today not to work ( yes, it chose to be an idiot and not work *VERY* grumpy face) so I can't upload a picture of my work. If I were to type out the following it think it would be very difficult to read SOOO I will try to make a description as friendly as possible.

    I have the equation x^2 + 3x + 7
    It has complex roots x = -2/3 + i√19 and x = -2/3 - i√19

    I try evaluating these roots by plugging them back in. I try it two ways, and I am only trying out right now the positive root. I am having a problem already at the x^2 term.

    THE PROBLEM:
    To multiply the positive root by itself, I first try the "from the ground up" method of just distributing, and eventually making a substitution of -1 for i^2. After making that substitution, the point is that I end up subtracting the term that had the i^2, from 9/4. After simplifying, I have real component -10/4 and complex component (-6i√19)/4

    The second way I try to evaluate x^2 term is by using the multiplication definition of complex numbers (a + bi)(c + di) = (ac - bd) + (bc + ad)i . This results in me ADDING the same kind of complex part to the same real part...and
     
  2. jcsd
  3. Nov 23, 2012 #2
    Both methods should work, everything you've computed so far is correct. If you add (3x+7) to what you've computed for x^2 you get 0.
     
  4. Nov 23, 2012 #3
    Sorry i misclicked and posted before I was finished. The new thread is right above.
     
  5. Nov 23, 2012 #4

    haruspex

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    Try -3/2 ± i√(19)/2
     
  6. Nov 25, 2012 #5
    Why is this in number theory? By the way, like haruspex noticed, you are working with the wrong roots, by using the quadratic formula you should have got
    [tex]\frac{-3}{2}\pm\frac{i\sqrt{19}}{2}[/tex]

    P.S. just practicing typing in latex
     
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