Within the framework of the complexity equals action and complexity equals volume conjectures, we study the properties of holographic complexity for rotating black holes. We focus on a class of odd-dimensional equal-spinning black holes for which considerable simplification occurs. We study the complexity of formation, uncovering a direct connection between complexity of formation and thermodynamic volume for large black holes. We consider also the growth-rate of complexity, finding that at late-times the rate of growth approaches a constant, but that Lloyds bound is generically violated.
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