How can one obtain (using Mathematica) all the solutions of an equation involving conjugates like for example [tex]z \bar{z}=1[/tex]. Although this equation is very simple, it seems that Mathematica is not able to handle it. I obtain:(adsbygoogle = window.adsbygoogle || []).push({});

Of course I'm not interested in this particularly simple equation, but of an equation involving many terms, which can't be, unfortunately, done by hand in a reasonable amount of time.Code (Text):

Solve[z Conjugate[z] == 1, z]

InverseFunction::ifun: Inverse functions are being used. Values may be lost for multivalued inverses. >>

Solve::tdep: The equations appear to involve the variables to be solved for in an essentially non-algebraic way. >>

Solve[z z^\[Conjugate]\[LongEqual]1,z]

Any ideas?

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# Solving a complex equation involving conjugates with Mathematica

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