The modulus of $1 + \cos \alpha + i \sin \alpha$ is
- A. $2 \sin \frac{\alpha}{2}$
- B. $2 \cos \frac{\alpha}{2}$
- C. $\sin² \frac{\alpha}{2} - 1$
- D. $\cos² \frac{\alpha}{2} - 1$
Answer: B. $2 \cos \frac{\alpha}{2}$
Explanation: $|z| = \sqrt{(1+\cos\alpha)^2 + \sin²\alpha} = \sqrt{2+2\cos\alpha} = \sqrt{2(1+\cos\alpha)} = \sqrt{2(2\cos²(\alpha/2))} = 2\cos(\alpha/2)$.