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Math Help - Complex number, region

  1. #1
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    Complex number, region

    Can someone please draw for me the shaded region represented by:

    Arg(z) <= -5 PI/6

    I'm having trouble visualizing. (note that -PI < Arg(z) <= PI)

    I'm thinking its either the region from the positive Re(z) axis, clockwise to -5PI/6, or perhaps everything except the region from -5 PI/6 -> PI.

    I'm not sure.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by scorpion007 View Post
    Can someone please draw for me the shaded region represented by:

    Arg(z) <= -5 PI/6

    I'm having trouble visualizing. (note that -PI < Arg(z) <= PI)

    I'm thinking its either the region from the positive Re(z) axis, clockwise to -5PI/6, or perhaps everything except the region from -5 PI/6 -> PI.

    I'm not sure.
    It is the second of these. Consider the a point z with Arg(z)=-5.5 pi/6,
    this is in the region you want as:

    -5.5 pi/6 < -5 pi/6.

    While:

    -4.5 pi/6 > -5 pi/6

    and so is not in the required region.

    RonL
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  3. #3
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    ah thanks, i think i get it.

    So that means Arg(z) <= -5/6 PI lies in the 3rd quadrant, and is the region from -5/6PI to -PI ?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by scorpion007 View Post
    ah thanks, i think i get it.

    So that means Arg(z) <= -5/6 PI lies in the 3rd quadrant, and is the region from -5/6PI to -PI ?
    Yes.

    RonL
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