For a ∈ C, let A ={z ∈ C: Re (a+z̄)> Im (ā+z)} and B ={z ∈ C: Re (a+z̄)< Im (ā+z)}. Then among the two statements: (S1): If Re (a), Im (a)>0, then…

For $\displaystyle a \in \mathbb{C}$, let $\displaystyle \mathrm{A}=\{z \in \mathbb{C}: \operatorname{Re}(a+\bar{z})>\operatorname{Im}(\bar{a}+z)\}$ and $\displaystyle \mathrm{B}=\{z \in \mathbb{C}: \operatorname{Re}(a+\bar{z})<\operatorname{Im}(\bar{a}+z)\}$. Then among the two statements: (S1): If $\displaystyle \operatorname{Re}(a), \operatorname{Im}(a)>0$, then the set A contains all the real numbers (S2) : If $\displaystyle \operatorname{Re}(a), \operatorname{Im}(a)<0$, then the set B contains all the real numbers,