The statement is true.

The Möbius transformation $f(z) = \frac{z - i}{z + i}$ maps the circle $|z| = 1$ (the unit circle) to another circle. Möbius transformations generally map circles and lines in the complex plane to other circles and lines, with the unit circle often being transformed into a circle (though in some cases it might become a line).

If you want to explore this further or confirm details with a more specific derivation, feel free to ask!

---

Here are five related questions to expand on this:

1. How do you derive the image of the unit circle under a Möbius transformation?
2. What are the general properties of Möbius transformations?
3. How does a Möbius transformation map the entire complex plane?
4. Can a Möbius transformation map a line to a circle?
5. How do fixed points behave under a Möbius transformation?

Tip: Möbius transformations can always be written as $f(z) = \frac{az + b}{cz + d}$, and their properties are greatly influenced by the coefficients $a, b, c, d$.