Consider
SolveValues[z^3 == (1 - I) Sqrt[2], z] // AbsArg
{{2^(1/3), -(\[Pi]/12)}, {2^(1/3),
Arg[-(-1)^(1/3) (1 - I)^(1/3)]}, {2^(1/3),
Arg[(-1)^(2/3) (1 - I)^(1/3)]}}
The first root is presented in the expected polar form of a complex number. But Arg has trouble with the other two roots because SolveValues (Solve is the same) doesn't seem to complete the solution (leaving ^(1/3)) behind.
This should be easy. Any suggestions to obtain the expected roots of complex numbers?