An identity you can't formally conjugate: Out[9]= ProductLog[1,-1/2-I Log[π]/π]==I π/2-Log[π] In[10]:= Conjugate/@% Out[10]= Conjugate[ProductLog[1,-1/2-I Log[π]/π]]==-I π/2-Log[π] Why did it chicken out on the lhs? OK, we'll do it manually. In[11]:= %%/.I->-I Out[11]= ProductLog[1,-1/2-I Log[π]/π]==I π/2-Log[π] Nothing happened! This is because I is not a Symbol: In[12]:= FullForm[{-I,I/2}] Out[12]//FullForm= List[Complex[0,-1],Complex[0,Rational[1,2]]] OK, dammit, In[13]:= %%/.Complex[x_,y_]->x-I*y Out[13]= False Whaddya mean False?? OK, paralyze the = sign: In[14]:= MapAt[HoldForm,%%%,0] Out[14]= Equal[ProductLog[1,-1/2-I Log[π]/π],I π/2-Log[π]] In[15]:= %/.Complex[x_,y_]->x-I*y Out[15]= Equal[ProductLog[1,-1/2+I Log[π]/π],-I π/2-Log[π]] Yes! Why was this so hard? Now unfreeze the = sign: In[16]:= ReleaseHold[%] Out[16]= False To quote a certain duck, WAK! Spoiler: Conjugating this requires a change of branch: In[17]:= ReleaseHold[MapAt[-#&,%%,{1,1}]] Out[17]= ProductLog[-1,-1/2+I Log[π]/π]==-I π/2-Log[π] which is what In[10] Conjugate would have said, had it been smarter. --rwg