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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.

    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


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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

    P.S. just practicing typing in latex
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