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Homework Help: Complex numbers question ;)

  1. Mar 11, 2010 #1
    1. The problem statement, all variables and given/known data

    One root of the equation x^2 + ax + b = 0 is 4 + 5i.

    Write down the second root.

    2. Relevant equations


    3. The attempt at a solution

    My problem is it's a "write down" question which suggests no working required. This is probably so simple but I just don't know... I cannot do this even thought I know the later parts of the question. Thank you in advance ;)
  2. jcsd
  3. Mar 11, 2010 #2


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    Write down the quadratic equation as you know it. The quadratic formula gives you two equations using one formula. What changes about the formula that gives you 2 separate solutions?
  4. Mar 11, 2010 #3
    The plus or minus, so would it be 4 - 5i?
  5. Mar 11, 2010 #4


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    Yup! The quadratic formula gives solutions as

    \frac{{ - b}}{{2a}} \pm \frac{{\sqrt {b^2 - 4ac} }}{{2a}}

    However, you can rewrite the quadratic formula by pulling out a -1 from the term in the square root to get

    \frac{{ - b}}{{2a}} \pm i\frac{{\sqrt {4ac - b^2 } }}{{2a}}

    So you can identify the 4 and the 5 with the real and imaginary parts of the equation.
  6. Mar 11, 2010 #5
    Hehe, thank you so much :)

    I know it was rather simple but my mind just wouldn't trigger.

    Ty again ;)
  7. Mar 13, 2010 #6


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    By the way, that answer is correct only if [itex]a[/itex] and [itex]b[/itex] are both real. If the problem doesn't specify that they are, then the other root could be any complex number.
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