Hydrazine, N₂H₄(aq), is used in the preparation of polymers, pharmaceuticals and rocket fuel.  Hydrazine has alkaline properties similar to ammonia and will act as a weak base.  Given that a 100 mL sample of 0.10 mol/L hydrazine solution has a pH of 10.55 at 25.0 ^oC, write the formula for the conjugate acid and calculate the Ka of the conjugate acid.