Clear["Global`*"]​​​​lineLoad=F1+I*F2;​​poissonR=ν;​​modulusE=;​​​​(*ComplexPotentialFunctions*)​​Ω=-((lineLoad/(8*Pi*(1-poissonR))))*Log[z]​​ω=(((lineLoad*(3-(4*poissonR)))/(8*Pi*(1-poissonR))))*Log[z]​​​​​​displacement=((1+poissonR)/modulusE)*ComplexExpand[((3-4*poissonR)*Ω)-(z*Conjugate[D[Ω,z]])-(Conjugate[ω]),TargetFunctions->Conjugate]//FullSimplify​​u1=ComplexExpand[Re[displacement],TargetFunctionsConjugate]/.z->r*(E^(I*θ))//FullSimplify​​u2=ComplexExpand[Im[displacement],TargetFunctionsConjugate]/.z->r*(E^(I*θ))//FullSimplify