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Solving in the form a+bi

  1. Apr 23, 2009 #1
    1. The problem statement, all variables and given/known data

    x^2 + (1-i)x + (-6 + 2i) = 0, solve in terms of a + bi

    2. Relevant equations

    3. The attempt at a solution

    Here's what I have so far... But I could be wrong.

    x = -(x-xi) +/- sqrt[ (x-xi)^2 - 4(-6 + 2i) ] / 2

    x = -(x-xi) +/- sqrt[ (x^2 - 2xi + xi^2) + 24 - 8i ] / 2

    I'm having trouble simplifying this part. Did I do something wrong?
     
  2. jcsd
  3. Apr 23, 2009 #2
    Remember that x should not be on the right hand side of the equation; b is just 1-i, not (1-i)*x.
     
  4. Apr 23, 2009 #3
    Ohhhh snap. Let me try again.
     
  5. Apr 23, 2009 #4
    So now I get to

    -(1 - i) +/- sqrt[ 25 - 10i + i^2 ] / 2

    And again, I'm stuck on the simplification.
     
  6. Apr 23, 2009 #5

    djeitnstine

    User Avatar
    Gold Member

    Check for factors, you have another quadratic under the root
     
  7. Apr 24, 2009 #6
    So I factor that to (i - 5)^2 and get:

    -(1 - i) +/- (i -5) / 2...
     
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