For a number of the form $a+\sqrt{b}$ where a,b are rational and $\sqrt{b}$ is not rational, its conjugate is $a-\sqrt{b}$. Both these numbers have minimal polynomial ${\left(x-a\right)}^2-b$. More generally, the conjugates of an algebraic number are the algebraic numbers with the same minimal polynomial. For example, the primitive fifth roots of unity are all conjugate, having the minimal polynomial x⁴ + x³+ x²+ x + 1.