gonio[z_] := {Abs[z], Arg[z]/Degree/1. }

gonio[1 + I]

ungonio[abs_, arg_] := abs*Exp[1. *I*Degree*arg]

ungonio[(Sqrt[2]), 45]

gonio2[z_] := 
      Print[Abs[z], "(cos(", Arg[z]/Degree/
          1. , ") + i*sin(", Arg[z]/Degree/1. , "))"]

gonio2[1 + I]