I am told that |z1-z2| is the distance between two points z1 and z2 in the complex plane. I have to give a geometric argument that(adsbygoogle = window.adsbygoogle || []).push({});

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

b)|z-1|=|z+i| represents the line through the origin whose slope is -1

Now my question is what exactly is a geometric argument, and what is sufficient in showing what I am told to show?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Geometric arguments

**Physics Forums | Science Articles, Homework Help, Discussion**