In[]:=
Simplify[Conjugate[
-*w*x

+
-1**w*x

],Assumptions->{w∈Reals,x∈Reals}]
Out[]=
2
wx

Simplify[Conjugate[
-*w*x

+
-4**w*x

],Assumptions->{w∈Reals,x∈Reals}](*Iexpect
wx

+
4iwx

*)
Out[]=
Conjugate[
-wx

+
-4wx

]