Solve[Abs[z]²==1,z]
returns two solutions, -1, and 1. I would like to get all the solutions of the
form Exp[I c₁].
Solve[Abs[z]²==1,z,Complexes]
Does not help either.
I can do
Solve[z Conjugate[z]==1,z,Complexes]
But then Mathematica complains about the solution containing a full-dimensional component.
Obviously the purpose of the question here isn't to characterize the solution (which is known) but to learn a little more about how Mathematica internals think about this.
Reducerather thanSolvein such cases. More on this topic one can find here What is the difference between Reduce and Solve? – Artes Nov 27 '22 at 23:442is wrong. – cvgmt Nov 28 '22 at 00:31