Load is Complex (Impedance):

Load current

i _L   =     V_TH /(R_TH + R) + j ( X_TH + X )

Magnitude of load current

| i_L | = V_TH /(R  _TH + R)² + ( X_TH + X )²

Load power P_L = | i_L |² × R

= (V_TH / (R_TH + R)² + ( X_TH+ X )²  )× R

For getting the maximum power of P_L, denominator of equation should be small.

For that select X = - X_th.

Then

P_L =( (V_TH )² / (R_Th+ R)² )× R

⇒ dP/ dl =0   ⇒R = R_TH

So, for maximum power factor

Z = R_TH -  j X _TH     = Z_TH

 (Complex conjugate of Z_TH)