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Questions on exact, symmetric reversal of a definition or functional mapping (i.e. the original form is returned when applied twice). Use this tag for issues on inversion of Mathematica expressions, or general inversion of math constructs.
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Is there an inverse function for F[x] = {Cos[x], Sin[x]} in Mathematica?
You can use this
Arg[#1 + I*#2] &[a, b]