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Shading in Argand diagrams involving inequalities

  1. May 16, 2016 #1
    1. The problem statement, all variables and given/known data
    What is difference in shading between Argand diagrams containing inequalities with > and ≥ signs?
    Shade the appropriate region to satisfy the inequality
    |z|> 5
    |z|≥ 5

    3. The attempt at a solution
    I am aware of the fact that both will have circle centered at origin with radius 5. But how will the shading differ in both inequalities?
  2. jcsd
  3. May 16, 2016 #2


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    For simplicity, think of a number line.
    With a strict inequality, the boundary may not be included.
  4. May 16, 2016 #3


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    For your example:

    In the ##\ | z | >5\ ## case, the boundary is not included in the region.

    In the ##\ | z | \ge 5\ ## case, the boundary is included in the region.

    This distinction is often indicated on any two-dimensional display by using a dashed or dotted line for any boundary element which is not included in the set and a solid line for any boundary element which is included in the set.
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