3 ms·
From the POV of this explanation, it's then quite fortuitous that the complexes are just two-dimensional over the reals, and can thus be easily visualized. That
by throwaway080383 8y ago
From the POV of this explanation, it's then quite fortuitous that the complexes are just two-dimensional over the reals, and can thus be easily visualized. That is, as soon as you adjoin the roots of x^2 + 1, and close under field operations, you actually get the roots of all polynomials.
- ginnungagap 8y agoThere is a deep result stating that for a field F there are only three possibilities for what the dimension of its algebraic closure can be as an F-vector space: it can be 1, if F is algebraically closed, it can be 2, as happens for R and other real closed fields, or it can be infinite, as it happens for Q, but there is no other option!