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Solve an equation with complex numbers

  1. Dec 7, 2011 #1
    1. The problem statement, all variables and given/known data
    I am doing a problem where I have to design a controller for a system. I have to solve the below equation for ω

    3.1 (ω)^2 - 6.2iω - 20

    2. Relevant equations



    3. The attempt at a solution

    I am not sure how to start It looks like a quadratic but I don't know what to do with the i
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 7, 2011 #2
    Looks like a quadratic, quacks like a quadratic. It is probably quadratic. You can use all the normal methods to solve it. The i is just part of the coefficient of the linear term.
     
  4. Dec 7, 2011 #3

    micromass

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    I can't really see an equation anywhere. All I see is an expression in [itex]\omega[/itex]. An equation must contain an "=".
     
  5. Dec 7, 2011 #4

    HallsofIvy

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    Yes, that's a quadratic. What it isn't is an equation! What is the problem really? Do you know the quadratic formula?
     
  6. Dec 7, 2011 #5
    Sorry, I thought he meant to factor it. Good point!
     
  7. Dec 7, 2011 #6
    Ok, it's the "i" that's causing the problem for him. That's intimidating to a lot of students not familiar with complex variables.

    The think to do 2slow is not be intimidated by them. Treat them just like constants but remember the complex arithmetic i times i is minus one. So you have:

    [tex]w^2-6.2iw-20=0[/tex]

    (I heard a quack)

    alright, that 6.2i is just a constant. Treat it just like if you were solving:

    [tex]w^2-aw-20=0[/tex]

    as long as you remember to do the complex arithmetic with i's so:

    [tex]w=\frac{6.2i\pm\sqrt{(6.2i)^2+80}}{2}[/tex]

    Not gonna' have problems with that (6.2i)^2 thing right?
     
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