Number of points having integral coordinates

In summary, the conversation is about the number of points with integral coordinates in the region A ∩ B ∩ C, where A, B, and C are sets of complex numbers defined by given equations. The solution is found to be 4, but upon further examination, it is corrected to be 6 points. The correction is made by carefully graphing the region and including boundary points in the given regions.
  • #1
utkarshakash
Gold Member
854
13

Homework Statement


Let A,B,C be three sets of complex numbers as defined below

A = {z:|z+1|[itex]\leq[/itex]2+Re(z)}, B = {z:|z-1|[itex]\geq[/itex]1} and
C=[itex]\left\{z: \frac{|z-1|}{|z+1|}\geq 1 \right\}[/itex]

The number of point(s) having integral coordinates in the region [itex]A \cap B \cap C[/itex] is

Homework Equations



The Attempt at a Solution


I worked out and found that [itex]A \cap B \cap C[/itex] is the area bounded by the parabola [itex]y^{2}=2(x+\frac{3}{2})[/itex] and the Y-axis. So the points having integral coordinates in this region are (-1,0), (0,0), (-1,1) and (-1,-1) which counts up to 4. But the correct answer is 6.
 
Physics news on Phys.org
  • #2
Get out a piece of graph paper and carefully graph your region. Note that boundary points are included in the given regions.
 
  • #3
jambaugh said:
Get out a piece of graph paper and carefully graph your region. Note that boundary points are included in the given regions.

Ughhh... How can I miss (0,-1) and (0,1)! Thanks.
 

1. What is the meaning of "Number of points having integral coordinates"?

The "Number of points having integral coordinates" refers to the total number of points on a graph or grid that have both an x and y coordinate that are whole numbers, or integers.

2. How is the number of points having integral coordinates calculated?

The number of points having integral coordinates can be calculated by using the formula n * (n+1), where n is the number of units on each side of the graph or grid. For example, if a graph has 5 units on each side, the number of points with integral coordinates would be 5 * (5+1) = 30.

3. Can the number of points having integral coordinates be negative?

No, the number of points having integral coordinates cannot be negative. This is because it represents a count of the actual points on a graph, and negative points do not exist.

4. Why is the concept of "Number of points having integral coordinates" important?

The concept of "Number of points having integral coordinates" is important in various mathematical and scientific fields, such as geometry, graph theory, and computer science. It is used in calculations and problem-solving, and helps to understand the properties and patterns of different graphs and grids.

5. Is there a relationship between the number of points having integral coordinates and the shape of a graph?

Yes, there is a relationship between the number of points having integral coordinates and the shape of a graph. For example, a graph with a larger area will generally have a higher number of points with integral coordinates compared to a graph with a smaller area. Additionally, the number of points with integral coordinates may also vary depending on the type of graph or grid, such as a Cartesian plane versus a polar coordinate system.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
20
Views
2K
  • Precalculus Mathematics Homework Help
Replies
5
Views
761
  • Precalculus Mathematics Homework Help
Replies
8
Views
319
  • Precalculus Mathematics Homework Help
Replies
7
Views
822
  • Precalculus Mathematics Homework Help
Replies
5
Views
925
  • Precalculus Mathematics Homework Help
Replies
8
Views
1K
  • Precalculus Mathematics Homework Help
Replies
6
Views
1K
  • Precalculus Mathematics Homework Help
Replies
9
Views
1K
  • Precalculus Mathematics Homework Help
Replies
29
Views
1K
  • Precalculus Mathematics Homework Help
Replies
3
Views
1K
Back
Top