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Arguement - complex numbers

  1. Dec 9, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the modulus and the principal value of the argument for the complex number [tex]\sqrt{3}[/tex] - i

    3. The attempt at a solution

    I know the modulus is just 'square both, add, and square root of sum', so r = [tex]\sqrt{2}[/tex], but I don't know how to find the second part. I know vaguely that the argument = [tex]\theta[/tex], but I don't know where to go from here.

    Do I need to convert the complex number into polar or euler form?
  2. jcsd
  3. Dec 9, 2009 #2


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    Homework Helper

    What two numbers did you 'square both, add, and square root of sum' to get sqrt(2)? The complex number a+bi can be drawn as the hypotenuse of a right triangle in the complex plane with a horizontal leg of length a and a vertical leg of length b. Haven't you seen this picture? The argument is the angle the hypotenuse makes with the x-axis. So you have tan(argument)=b/a. Remember trig? Principal value is a convention for choosing which of several possible angles might satisfy the tangent equation. Look it up, hopefully it will come with a nice picture.
  4. Dec 9, 2009 #3
    okay, I think I get the argument now

    for the modulus, I added [tex]\sqrt{3}[/tex] [tex]^{2}[/tex] and i[tex]^{2}[/tex] to get 3 - 1, then square rooted to get [tex]\sqrt{2}[/tex]

    is that wrong?
  5. Dec 9, 2009 #4


    Staff: Mentor

    Yes. You square the real part, sqrt(3), and the imaginary part, -1, add them, then take the square root. The imaginary part is the coefficient of i.
  6. Dec 9, 2009 #5
    okay, thanks
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