Sziklai pair and Darlington pair input impedence
Here is my answer for the Darlington combination (input resistance hie,D):


hie,D=hie,3 + hfe,3*hie,1 (the input resistance of Q1 appears at the base of Q3 multiplied with the current gain)
We have hie,1=hfe,1/gm1 with gm1=gm,3*hfe,1 (because Ic1=hfe,1*Ic3).
From this: hie,D=hie,3 + hfe,3/gm,3= 2*hie,3


Hence, the input resistance of the darlington transistor is twice the input resistance of the first transistor (Q3)