The structured singular value mu measures the robustness of uncertain systems. Numerous researchers over the last decade have worked on developing efficient methods for computing mu. This paper considers the complexity of calculating mu with general mixed real/complex uncertainty in the framework of combinatorial complexity theory. In particular, it is proved that the mu recognition problem with either pure real or mixed real/complex uncertainty is NP-hard. This strongly suggests that it is futile to pursue exact methods for calculating mu of general systems with pure real or mixed uncertainty for other than small problems.