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Math Help - Sketching regions in the complex plane

  1. #1
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    Sketching regions in the complex plane

    Hi all I have the following problem:

    Sketch the following region in the complex plane:

    |z+1+i| greater than or equal to 1

    i worked through the problem and got the solution (x+1)^2 + (y+1)^2 greater than or equal to 1^2

    My question is: how is a circle of radius 1 possibly going to be greater than its own radius? if i'm completely wrong, what does the 1^2 represent other than the radius of the circle?
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  2. #2
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    Re: Sketching regions in the complex plane

    |z+1+i| >= 1

    |z-(-1-i)| >= 1

    The distance from -1-i is greater than or equal to 1. This is not a circle. It is an entire plane with an open circle removed.

    You are close. Your circle is the edge of the solution region. Excepting the switch to cartesian coordinates, your work seems reasonable.
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    Re: Sketching regions in the complex plane

    Quote Originally Posted by andrew2322 View Post
    Hi all I have the following problem:

    Sketch the following region in the complex plane:

    |z+1+i| greater than or equal to 1

    i worked through the problem and got the solution (x+1)^2 + (y+1)^2 greater than or equal to 1^2

    My question is: how is a circle of radius 1 possibly going to be greater than its own radius? if i'm completely wrong, what does the 1^2 represent other than the radius of the circle?
    The solution is the circle \displaystyle (x + 1)^2 + (y + 1)^2 = 1 and all points outside the circle as well.
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