height of an algebraic number

Suppose we have an algebraic number such that the polynomial of smallest degree it is a root of (with the co-efficients relatively prime) is given by:

$$\sum _{i=0}^n{a}_i{x}^i.$$

Then the height $h$ of the algebraic number is given by:

$$h=n+\sum _{i=0}^n|a_i|.$$

This is a quantity which is used in the proof of the existence of transcendental numbers.