I'm trying to integrate around a path defined below in the complex plane. I understand that if the region enclosed by the curve contains an isolated singularity then the value of the integral can be computed using Cauchy's Integral Formula. The problem I'm having is understanding the path in the real/imaginary plane.
Q: For $z,$ $z_0$, $z_1$ $\in{\mathbb{C}}$, how is the curve defined by $|z-z_{0}|+|z-z_{1}| = k,$ $k\in{\mathbb{R}}, n\in{\mathbb{N}}$ represented on the real/imaginary plane? In general, is there a particular graphic representation of $|z-z_{0}| + |z-z_{1}| + \dots + |z-z_{n}| = k$, $k\in{\mathbb{R}}$ in the Re(z)/Im(z) plane? Concretely, the path I'm given is this: $|z-2|+|z+2|=10$.
Attempt at Ans: I understand that for $z$, $z_0\in{\mathbb{C}}$, $|z-z_0|=k$, $k\in{\mathbb{R}}$ represents a circle of radius k, but I'm not sure what happens when you take the sum of multiple moduli of z.