\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(a, b, c \in \mathbb{R}\) with \((a, b) \ne (0, 0)\). Show that the half-plane \(H = \{x + iy \in \mathbb{C} : ax + by < c\}\) is open in \(\mathbb{C}\).
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