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Complex Number (Modulus/Phase)

  1. Nov 2, 2008 #1


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    1. The problem statement, all variables and given/known data
    Equation: [itex]\frac{z\theta_0^2}{-\theta^2+ 2i\theta\theta_0\phi+\theta_0^2}[/itex]

    Where [itex]z, \ \phi[/itex] are constant and [itex]\theta_0[/itex] is the initial theta. Find the modulus and the phase associated with this equation.

    2. Relevant equations
    [itex]\frac{z\theta_0^2}{-\theta^2+ 2i\theta\theta_0\phi+\theta_0^2}[/itex]

    3. The attempt at a solution
    To find the modulus, I seperated the equation into real and imaginary and multiplied by the conjugate of the imaginary number to get it in the numerator and I got: [itex]=\frac{z\theta^2\phi - z\theta_0^2\phi}{\theta\phi} - \frac{z\theta_0}{2\theta\phi}i[/itex]. When doing the modulus, I get: [itex]\sqrt{\frac{4z^2\phi^2\theta^4-8\phi^2z^2\theta^2\theta_0^2+ 4z^2\theta_0^4\phi^2 +z^2\theta_0^2}{4\theta^2}\phi^2}[/itex] and this doesn't seem to simplify too well. Have I made a mistake or is there an easier method which I have missed? :confused: Thanks in advance for the help.
    Last edited: Nov 2, 2008
  2. jcsd
  3. Nov 2, 2008 #2


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    Science Advisor

    Modulus and phase apply to a single complex number. What do you mean by "modulus and phase associated with this equation"?

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