Changes

*<math>-\frac{1}{2} - \frac{\sqrt{3}}{2}i\,</math>

*<math>-\frac{1}{2} - \frac{\sqrt{3}}{2}i\,</math>

One can verify that

One can verify that

<math>(x-1) (x + \frac{1}{2} - \frac{\sqrt{3}}{2}i) (x + \frac{1}{2} + \frac{\sqrt{3}}{2}i) = x^3 - 1\,</math>

<math>(x-1) \left(x + \frac{1}{2} - \frac{\sqrt{3}}{2}i\right) \left(x + \frac{1}{2} + \frac{\sqrt{3}}{2}i\right) = x^3 - 1\,</math>

For a given field, the field containing it (strictly speaking, the smallest such field) that is algebraically closed is called its algebraic closure.  The field of real numbers is not algebraically closed; its closure is the field of complex numbers.

For a given field, the field containing it (strictly speaking, the smallest such field) that is algebraically closed is called its algebraic closure.  The field of real numbers is not algebraically closed; its closure is the field of complex numbers.