>>12510701The multiset of nth roots of a non-zero complex number has no multiplicities greater than 1.
Take any nth root of your non-zero complex number, and multiply it to each nth root of unity.
Because the complex numbers are a field, you will get n distinct roots for your complex number. By the fundamental theorem of algebra, there can’t exist any other roots, so you have described the set.
The space would just be the complex numbers, as any set of two or more single dimension complex vectors, with complex coefficients, is necessarily linearly dependent.
