  We investigate how well complex algebraic numbers can be approximated by
algebraic numbers of degree at most n. We also investigate how well complex
algebraic numbers can be approximated by algebraic integers of degree at most
n+1. It follows from our investigations that for every positive integer n there
are complex algebraic numbers of degree larger than n that are better
approximable by algebraic numbers of degree at most n than almost all complex
numbers. As it turns out, these numbers are more badly approximable by
algebraic integers of degree at most n+1 than almost all complex numbers.
