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.
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