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Math Help - Problems solving argument?

  1. #1
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    Problems solving argument?

    Arg\left (\frac{i\omega}{2-i\omega} \right )=Arg(i\omega)-Arg(2-i\omega)

    Solution:
    \pi-arctan\left (\frac{\omega}{2} \right )
    \omega>0

    My attempt:

    Arg(i\omega)=\frac{\pi}{2}

    Arg(2-i\omega)=-arctan\left (\frac{\omega}{2} \right )

    Arg(i\omega)-Arg(2-i\omega)=\frac{\pi}{2}-\left (-arctan\left (\frac{\omega}{2} \right ) \right )=\frac{\pi}{2}+arctan\left (\frac{\omega}{2} \right )

    Can somebody explain why the solution differs from my solution?
    I have tested Arg(iw) with any number w>0 and they all give me pi/2?

    Also I don't understand how they got the subtraction when mine ends up being a sum?
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  2. #2
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    Re: Problems solving argument?

    Hey MathIsOhSoHard.

    Can you take the tangent of both sides (since arg is in terms of arctan) and simplify that way?
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