# Complex variables : Triangle inequality

1. Aug 25, 2008

### Benzoate

1. The problem statement, all variables and given/known data

Using the fact that |z(1)-z(2)| is the distance between two points z(1) and z(2) , give a geometric argument that

a)|a-4*i| + |z+4*i| =10 represents an ellipse whose foci are (0,4) and(0,-4).

2. Relevant equations

Triangle inequality equation; distance formula

3. The attempt at a solution

|z(1)-z(2)|=sqrt((0-0)^2 + (4-(-4))^2)= 8 . How is the Radius =10 of the equation related to the distance between z(1) and z(2) which I calculated to be 8. If there is a relationship between the distance formula and the radius, how will the relationship between the radius and the distance between the two points help me determined if|z-4i| + |z+4i|=10 represents an ellipse with foci (0,4) and (0,-4).

2. Aug 25, 2008

### NoMoreExams

You calculated the distance between the foci didn't you? The foci don't lie on the contour of the ellipse. Besides how are you defining radius for an ellipse?

3. Aug 25, 2008

### Benzoate

I don't think there is a radius for an ellispse. But what variable of the ellipse is 10 supposed to represent? distance between the foci is 8.