Let C be the set of complex numbers. What kind of a mapping defines $f\; :\;C \rightarrow R\;given\;by\;f(z)=|\;z\;|,\forall\; z \in C$?

related to an answer for: Let C be the set of complex numbers.Prove that the mapping $f\; :\;C \rightarrow R\;given\;by\;f(z)=|\;z\;|,\forall\; z \in C,$is neither one-one nor onto.

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