Answer is: pH of hydrazine conjugate acid is 4.088.
Chemical reaction: N₂H₅⁺ + H₂O ⇄ N₂H₄ + H₃O⁺.
[N₂H₅⁺] = 2.0 M.
[N₂H₄] = [H₃O⁺] = x.
Kb(N₂H₄) = 3.0·10⁻⁶.
Kb·Ka = 1.00·10⁻¹⁴.
Ka(N₂H₅⁺) = 1.00·10⁻¹⁴ ÷ 3.0·10⁻⁶.
Ka = 3.33·10⁻⁹.
Ka = [N₂H₄]·[H₃O⁺] / [N₂H₅⁺].
3.33·10⁻⁹ = x² / 2.0 M.
x = [H₃O⁺] = √3.33·10⁻⁹ · 2.0 M.
[H₃O⁺] = 8.1·10⁻⁵ M.
pH = -log[H₃O⁺].
pH = -log(8.1·10⁻⁵ M).
pH = 4.088.