The upper half-plane is the portion of the complex plane {x + i y:x, y element (-∞, ∞)} satisfying y = ℑ[z]>0 i.e., {x + i y:x element (-∞, ∞), y element (0, ∞)}. Common notations include H, H, H^+, and ℋ. The notation H^* or ℋ^* is sometimes used to denote H union {i∞} union Q.

complex plane | half-plane | left half-plane | lower half-plane | modular function | right half-plane | upper half-disk