In complex analysis, the (open) right half-plane is the set of all points in the complex plane whose real part is strictly positive, that is, the set { z ∈ C : Re ( z ) > 0 } {\textstyle \{z\in \mathbb {C} \,:\,{\mbox{Re}}(z)>0\}} .
References Rudin, W., Real and Complex Analysis, 3 ed. (McGraw-Hill, 1986). Ahlfors, L., Complex Analysis, 3 ed. (McGraw-Hill, 1979). Kato, T., Perturbation theory for linear operators, 2 ed. (Springer-Verlag, 1995)