Let \(S=\left\{z\in\mathbb{C}:\ \overline z=i\big(z^2+\operatorname{Re}(\overline z)\big)\right\}\). Then \(\displaystyle\sum_{z\in S}\lvert z\rvert^2\) is equal to :
\(\dfrac{7}{2}\)
\(4\)
\(\dfrac{5}{2}\)
\(3\)
