1. **Problem:** Find the modulus $|z|$ of the complex number $z = \frac{2 - i}{2 + i}$. 2. **Formula:** The modulus of a complex number $z = \frac{a}{b}$ is $|z| = \frac{|a|}{|b|}$ where $|a|$ and $|b|$ are the moduli of the numerator and denominator respectively. 3. **Calculate moduli:** - $|2 - i| = \sqrt{2^2 + (-1)^2} = \sqrt{4 + 1} = \sqrt{5}$ - $|2 + i| = \sqrt{2^2 + 1^2} = \sqrt{4 + 1} = \sqrt{5}$ 4. **Evaluate $|z|$:** $$|z| = \frac{|2 - i|}{|2 + i|} = \frac{\sqrt{5}}{\sqrt{5}} = 1$$ 5. **Answer:** The modulus $|z|$ is 1. Hence, the correct choice is c) 1.