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JEE Math Practice Question

Let $$S=\left\{z \in \mathbb{C}: \bar{z}=i\left(z^{2}+\operatorname{Re}(\bar{z})\right)\right\}$$. Then $$\sum\limits_{z \in \mathrm{S}}|z|^{2}$$ is equal to :

  1. A.$$\frac{7}{2}$$
  2. B.4
  3. C.3
  4. D.$$\frac{5}{2}$$

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