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Shading in Argand diagrams involving inequalities

  • #1
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Homework Statement


What is difference in shading between Argand diagrams containing inequalities with > and ≥ signs?
Example
Shade the appropriate region to satisfy the inequality
|z|> 5
|z|≥ 5

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?
 

Answers and Replies

  • #2
robphy
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For simplicity, think of a number line.
With a strict inequality, the boundary may not be included.
 
  • #3
SammyS
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Homework Statement


What is difference in shading between Argand diagrams containing inequalities with > and ≥ signs?
Example
Shade the appropriate region to satisfy the inequality
|z|> 5
|z|≥ 5

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?
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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