(adsbygoogle = window.adsbygoogle || []).push({}); 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).

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# Homework Help: Complex variables : Triangle inequality

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