1.NounA real or complex number (more generally, an element of a number field) which is a root of a monic polynomial whose coefficients are integers; equivalently, an algebraic number whose minimal polynomial (lowest-degree polynomial of which it is a root and whose leading coefficient is 1) has integer coefficients.
"A Gaussian integer
z
=
a
+
i
b
{\displaystyle z=a+ib}
is an algebraic integer since it is a solution of either the equation
z
2
+
(
−
2
a
)
z
+
(
a
2
+
b
2
)
=
0
{\displaystyle z^{2}+(-2a)z+(a^{2}+b^{2})=0}
or the equation
z
−
a
=
0
{\displaystyle z-a=0}
."