A complex number is said to be algebraic if it is a root of a polynomial with rational coefficients. Examples include , , , and . A number that is not algebraic is called a transcendental number, such as or .
Number of algebraic numbers
Algebraic numbers are studied extensively in algebraic number theory.
- All rational numbers are algebraic, but not all algebraic numbers are rational. For example, consider , which is a root of .
- The if a and b are algebriac than is either rational or transendental
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