The number of complex numbers $z$ with $|z| = 2$ satisfying $|z + \bar{z}| = |z - \bar{z}|$ is:
Step-by-Step Solution
Key Concept: $z + \bar{z} = 2 \operatorname{Re}(z)$ and $z - \bar{z} = 2i\operatorname{Im}(z)$. The condition forces $|\operatorname{Re}(z)| = |\operatorname{Im}(z)|$. Combine with $|z| = 2$.
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Correct Answer: (2)