An algebraic number is a type of number that is a solution to a polynomial equation with integer coefficients. For example, the number √2 is algebraic because it satisfies the equation x² - 2 = 0. Algebraic numbers can be either rational, like 1/2, or irrational, like √3. These numbers are part of a broader category known as complex numbers, which include all numbers that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit. Algebraic numbers are important in various fields of mathematics, including number theory and abstract algebra.