This seems like an elementary question, but I was unable to find an clear answer to it.
Generally, the real and imaginary parts of a complex number comprised of radicals are not expressible by radicals themselves (see for example Casus irreductibilis, which is a special case where the imaginary part is $0$).
However, a numerical approximation can be done to achieve arbitrary precision for the real and imaginary parts.
What's the general method for evaluating the real and imaginary parts of a complex number?
For an example, see here.
In the above example, an alternative form consisting of trigonometric functions is shown, which suggests that conversion to polar form is a way to go. Is this it?
Is this then also possible on even more complicated, non-algebraic, complex numbers, such as this one?