Novel broken symmetry states can spontaneously form due to Coulomb interactions in electronic systems with multiple internal degrees of freedom. A powerful approach to distinguish among these phases is to visualize their wave functions with a scanning tunneling microscope (STM). In this talk, I will describe measurements of bismuth surface states, where strong spin-orbit coupling leads to six degenerate teardrop-shaped hole pockets. Our spectroscopic measurements reveal that a combination of strain and exchange interactions fully lifts this degeneracy at high magnetic field. Using the STM to directly image the resulting wave functions, we identify the emergence of two recently predicted exotic quantum Hall phases. We observe a nematic quantum Hall liquid that spontaneously breaks the rotational symmetry of the underlying crystal lattice and a ferroelectric quantum Hall phase characterized by wave functions with an intrinsic dipole moment.