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We derive exact formulas for the frequency of synchronized oscillations in Kuramoto models with conformist-contrarian interactions, and determine necessary conditions for synchronization to occur. Numerical computations show that for certain parameters repulsive nodes behave as conformists, and that in other cases attractive nodes can display frustration, being neither conformist nor contrarian. The signs of repulsive couplings can be placed equivalently outside the sum, as proposed in Phys.doi:10.1088/0031-8949/89/11/115202 fatcat:5xzgg75zy5fpph6xkryxmfy2cq