The ionisation constant of ammonia and ammonium hydroxide is same
NH3+H2O→NH+4+OH−K1[NH+4][OH−]NH3
NH4OH→NH+4+OH−K2=[NH+4][OH−][NH4OH]
But [NH3]=[NH4OH] (this is because when ammonia is dissolved in water, it is converted to ammonium hydroxide).
Hence, K1=K2
Hence, the ionization constant of ammonia and ammonium hydroxide is same.