  We consider the problem of finding a best uniform approximation to the
standard monomial on the unit ball in $\bbC^2$ by polynomials of lower degree
with complex coefficients. We reduce the problem to a one-dimensional weighted
minimization problem on an interval. In a sense, the corresponding extremal
polynomials are uniform counterparts of the classical orthogonal Jacobi
polynomials. They can be represented by means of special conformal mappings on
the so-called comb-like domains. In these terms, the value of the minimal
deviation and the representation for a polynomial of best approximation for the
original problem are given. Furthermore, we derive asymptotics for the minimal
deviation.
