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Math Help - help with complex variables

  1. #1
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    help with complex variables

    I was given the problem:

    Sketch the following sets and determine which are domains:

    (a) \midz-2+i \mid < 1
    (b) \mid2z+3 \mid > 3
    (c) Im(z) > 1
    (d) Im(z) = 1
    (e) 0 < or equal to arg(z) > or equal to pi/4 and z not equal to 0
    (f) \midz-f \mid > or equal to \midz \mid

    I have no idea how to start this. I know you cannot show sketches on this, but can anyone give me ideas of what I am doing for this question?
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  2. #2
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    Quote Originally Posted by LCopper2010 View Post
    I was given the problem:

    Sketch the following sets and determine which are domains:

    (a) \midz-2+i \mid < 1
    (b) \mid2z+3 \mid > 3
    (c) Im(z) > 1
    (d) Im(z) = 1
    (e) 0 < or equal to arg(z) > or equal to pi/4 and z not equal to 0
    (f) \midz-f \mid > or equal to \midz \mid

    I have no idea how to start this. I know you cannot show sketches on this, but can anyone give me ideas of what I am doing for this question?
    If that is true, then why have you been asked to do these?
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  3. #3
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    Quote Originally Posted by LCopper2010 View Post
    I was given the problem:

    Sketch the following sets and determine which are domains:

    (a) \midz-2+i \mid < 1
    (b) \mid2z+3 \mid > 3
    (c) Im(z) > 1
    (d) Im(z) = 1
    (e) 0 < or equal to arg(z) > or equal to pi/4 and z not equal to 0
    (f) \midz-f \mid > or equal to \midz \mid

    I have no idea how to start this. I know you cannot show sketches on this, but can anyone give me ideas of what I am doing for this question?
    |z- a| is the distance form point z to point a in the complex plane. |z- 2+i|= |z- (2-i)| is the distance from the point 2-i to z. The set of all z such that that distance is equal to 1 is the circle with center at 2- i and radius 1. What does that tell you about |z-(2-i)|< 1 and |z-(2-i)|> 1?

    The imaginary part of z, Im(z), is the "y" coordinate on the complex plane so Im(z)= 1 is a horizontal line.
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