Complex Numbers

For \(a \in \mathbb{C}\), let \(\mathrm{A}=\{z \in \mathbb{C}: \operatorname{Re}(a+\bar{z}) > \operatorname{Im}(\bar{a}+z)\}\) and \(\mathrm{B}=\{z \in \mathbb{C}: \operatorname{Re}(a+\bar{z})<\operatorname{Im}(\bar{a}+z)\}\). Then among the two statements :

(S1): If \(\operatorname{Re}(a), \operatorname{Im}(a) > 0\), then the set A contains all the real numbers

(S2) : If \(\operatorname{Re}(a), \operatorname{Im}(a) < 0\), then the set B contains all the real numbers,