# Homework Help: Number of points having integral coordinates

1. Oct 15, 2012

### utkarshakash

1. The problem statement, all variables and given/known data
Let A,B,C be three sets of complex numbers as defined below

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

The number of point(s) having integral coordinates in the region $A \cap B \cap C$ is

2. Relevant equations

3. The attempt at a solution
I worked out and found that $A \cap B \cap C$ is the area bounded by the parabola $y^{2}=2(x+\frac{3}{2})$ 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.

2. Oct 15, 2012

### jambaugh

Get out a piece of graph paper and carefully graph your region. Note that boundary points are included in the given regions.

3. Oct 15, 2012

### utkarshakash

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