Describing Locus of Complex points

Question

Having trouble describing locus of complex points.

Not sure how to approach these types of questions. Do I just replace $|z|$ with $\sqrt{x^2+y^2}$ ?

The question: $|z+2| + |z-2| = 5$

Answer 1

An ellipse can be described as the locus of points the sum of whose distances from two points (the foci) is constant. Thus we have an ellipse with foci $(-2,0)$ and $(2,0)$.