Mark Dickinson <dicki...@gmail.com> added the comment:

BTW, to forestall questions about adding cmath.cbrt: it's not obvious how to 
extend the real cube root function to a complex cube root, so it might make 
sense to wait for actual use-cases before doing so.

The issue is that the most natural way to define a complex cube root would use 
a branch cut along the negative real axis (the same branch cut that cmath.sqrt 
and cmath.log use). But then the principal branch would *not* be an extension 
of math.cbrt: it would return non-real values on the negative real axis. (The 
*real* cube roots of negative numbers would fall on the two non-principal 
branches.)

See for example 
https://math.stackexchange.com/questions/71775/extending-the-cube-root-function-to-mathbbc

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<https://bugs.python.org/issue44357>
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